Daily Papers

Diffusion models have demonstrated exceptional capability in generating high-quality images, videos, and audio. Due to their adaptiveness in iterative refinement, they provide a strong potential for achieving better non-autoregressive sequence generation. However, existing text diffusion models still fall short in their performance due to a challenge in handling the discreteness of language. This paper thoroughly analyzes text diffusion models and uncovers two significant limitations: degradation of self-conditioning during training and misalignment between training and sampling. Motivated by our findings, we propose a novel Text Diffusion model called TREC, which mitigates the degradation with Reinforced Conditioning and the misalignment by Time-Aware Variance Scaling. Our extensive experiments demonstrate the competitiveness of TREC against autoregressive, non-autoregressive, and diffusion baselines. Moreover, qualitative analysis shows its advanced ability to fully utilize the diffusion process in refining samples.

Scaling visual generation models is essential for real-world content creation, yet requires substantial training and computational expenses. Alternatively, test-time scaling has garnered growing attention due to resource efficiency and promising performance. In this work, we present TTS-VAR, the first general test-time scaling framework for visual auto-regressive (VAR) models, modeling the generation process as a path searching problem. To dynamically balance computational efficiency with exploration capacity, we first introduce an adaptive descending batch size schedule throughout the causal generation process. Besides, inspired by VAR's hierarchical coarse-to-fine multi-scale generation, our framework integrates two key components: (i) At coarse scales, we observe that generated tokens are hard for evaluation, possibly leading to erroneous acceptance of inferior samples or rejection of superior samples. Noticing that the coarse scales contain sufficient structural information, we propose clustering-based diversity search. It preserves structural variety through semantic feature clustering, enabling later selection on samples with higher potential. (ii) In fine scales, resampling-based potential selection prioritizes promising candidates using potential scores, which are defined as reward functions incorporating multi-scale generation history. Experiments on the powerful VAR model Infinity show a notable 8.7% GenEval score improvement (from 0.69 to 0.75). Key insights reveal that early-stage structural features effectively influence final quality, and resampling efficacy varies across generation scales. Code is available at https://github.com/ali-vilab/TTS-VAR.

Visual Autoregressive (VAR) modeling has gained popularity for its shift towards next-scale prediction. However, existing VAR paradigms process the entire token map at each scale step, leading to the complexity and runtime scaling dramatically with image resolution. To address this challenge, we propose FastVAR, a post-training acceleration method for efficient resolution scaling with VARs. Our key finding is that the majority of latency arises from the large-scale step where most tokens have already converged. Leveraging this observation, we develop the cached token pruning strategy that only forwards pivotal tokens for scale-specific modeling while using cached tokens from previous scale steps to restore the pruned slots. This significantly reduces the number of forwarded tokens and improves the efficiency at larger resolutions. Experiments show the proposed FastVAR can further speedup FlashAttention-accelerated VAR by 2.7times with negligible performance drop of <1%. We further extend FastVAR to zero-shot generation of higher resolution images. In particular, FastVAR can generate one 2K image with 15GB memory footprints in 1.5s on a single NVIDIA 3090 GPU. Code is available at https://github.com/csguoh/FastVAR.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inference process that maps complex systems into a simplified representational space and models large jumps in time. To achieve this, we propose Time-lagged Information Bottleneck (T-IB), a principled objective rooted in information theory, which aims to capture relevant temporal features while discarding high-frequency information to simplify the simulation task and minimize the inference error. Our experiments demonstrate that T-IB learns information-optimal representations for accurately modeling the statistical properties and dynamics of the original process at a selected time lag, outperforming existing time-lagged dimensionality reduction methods.

Variance reduction (VR) techniques have contributed significantly to accelerating learning with massive datasets in the smooth and strongly convex setting (Schmidt et al., 2017; Johnson & Zhang, 2013; Roux et al., 2012). However, such techniques have not yet met the same success in the realm of large-scale deep learning due to various factors such as the use of data augmentation or regularization methods like dropout (Defazio & Bottou, 2019). This challenge has recently motivated the design of novel variance reduction techniques tailored explicitly for deep learning (Arnold et al., 2019; Ma & Yarats, 2018). This work is an additional step in this direction. In particular, we exploit the ubiquitous clustering structure of rich datasets used in deep learning to design a family of scalable variance reduced optimization procedures by combining existing optimizers (e.g., SGD+Momentum, Quasi Hyperbolic Momentum, Implicit Gradient Transport) with a multi-momentum strategy (Yuan et al., 2019). Our proposal leads to faster convergence than vanilla methods on standard benchmark datasets (e.g., CIFAR and ImageNet). It is robust to label noise and amenable to distributed optimization. We provide a parallel implementation in JAX.

Diffusion models deliver high-fidelity synthesis but remain slow due to iterative sampling. We empirically observe there exists feature invariance in deterministic sampling, and present InvarDiff, a training-free acceleration method that exploits the relative temporal invariance across timestep-scale and layer-scale. From a few deterministic runs, we compute a per-timestep, per-layer, per-module binary cache plan matrix and use a re-sampling correction to avoid drift when consecutive caches occur. Using quantile-based change metrics, this matrix specifies which module at which step is reused rather than recomputed. The same invariance criterion is applied at the step scale to enable cross-timestep caching, deciding whether an entire step can reuse cached results. During inference, InvarDiff performs step-first and layer-wise caching guided by this matrix. When applied to DiT and FLUX, our approach reduces redundant compute while preserving fidelity. Experiments show that InvarDiff achieves 2-3times end-to-end speed-ups with minimal impact on standard quality metrics. Qualitatively, we observe almost no degradation in visual quality compared with full computations.

We propose an inference-time scaling approach for pretrained flow models. Recently, inference-time scaling has gained significant attention in LLMs and diffusion models, improving sample quality or better aligning outputs with user preferences by leveraging additional computation. For diffusion models, particle sampling has allowed more efficient scaling due to the stochasticity at intermediate denoising steps. On the contrary, while flow models have gained popularity as an alternative to diffusion models--offering faster generation and high-quality outputs in state-of-the-art image and video generative models--efficient inference-time scaling methods used for diffusion models cannot be directly applied due to their deterministic generative process. To enable efficient inference-time scaling for flow models, we propose three key ideas: 1) SDE-based generation, enabling particle sampling in flow models, 2) Interpolant conversion, broadening the search space and enhancing sample diversity, and 3) Rollover Budget Forcing (RBF), an adaptive allocation of computational resources across timesteps to maximize budget utilization. Our experiments show that SDE-based generation, particularly variance-preserving (VP) interpolant-based generation, improves the performance of particle sampling methods for inference-time scaling in flow models. Additionally, we demonstrate that RBF with VP-SDE achieves the best performance, outperforming all previous inference-time scaling approaches.

We rethink test-time scaling laws from a practical efficiency perspective, revealing that the effectiveness of smaller models is significantly overestimated. Prior work, grounded in compute-optimality, overlooks critical memory access bottlenecks introduced by inference-time strategies (e.g., Best-of-N, long CoTs). Our holistic analysis, spanning models from 0.6B to 32B parameters, reveals a new Kinetics Scaling Law that better guides resource allocation by incorporating both computation and memory access costs. Kinetics Scaling Law suggests that test-time compute is more effective when used on models above a threshold than smaller ones. A key reason is that in TTS, attention, rather than parameter count, emerges as the dominant cost factor. Motivated by this, we propose a new scaling paradigm centered on sparse attention, which lowers per-token cost and enables longer generations and more parallel samples within the same resource budget. Empirically, we show that sparse attention models consistently outperform dense counterparts, achieving over 60 points gains in low-cost regimes and over 5 points gains in high-cost regimes for problem-solving accuracy on AIME, encompassing evaluations on state-of-the-art MoEs. These results suggest that sparse attention is essential for realizing the full potential of test-time scaling because, unlike training, where parameter scaling saturates, test-time accuracy continues to improve through increased generation. The code is available at https://github.com/Infini-AI-Lab/Kinetics.

Visual Autoregressive (VAR) modeling has garnered significant attention for its innovative next-scale prediction approach, which yields substantial improvements in efficiency, scalability, and zero-shot generalization. Nevertheless, the coarse-to-fine methodology inherent in VAR results in exponential growth of the KV cache during inference, causing considerable memory consumption and computational redundancy. To address these bottlenecks, we introduce ScaleKV, a novel KV cache compression framework tailored for VAR architectures. ScaleKV leverages two critical observations: varying cache demands across transformer layers and distinct attention patterns at different scales. Based on these insights, ScaleKV categorizes transformer layers into two functional groups: drafters and refiners. Drafters exhibit dispersed attention across multiple scales, thereby requiring greater cache capacity. Conversely, refiners focus attention on the current token map to process local details, consequently necessitating substantially reduced cache capacity. ScaleKV optimizes the multi-scale inference pipeline by identifying scale-specific drafters and refiners, facilitating differentiated cache management tailored to each scale. Evaluation on the state-of-the-art text-to-image VAR model family, Infinity, demonstrates that our approach effectively reduces the required KV cache memory to 10% while preserving pixel-level fidelity.

Time series models face significant challenges in scaling to handle large and complex datasets, akin to the scaling achieved by large language models (LLMs). The unique characteristics of time series data and the computational demands of model scaling necessitate innovative approaches. While researchers have explored various architectures such as Transformers, LSTMs, and GRUs to address these challenges, we propose a novel solution using RWKV-7, which incorporates meta-learning into its state update mechanism. By integrating RWKV-7's time mix and channel mix components into the transformer-based time series model Timer, we achieve a substantial performance improvement of approximately 1.13 to 43.3x and a 4.5x reduction in training time with 1/23 parameters, all while utilizing fewer parameters. Our code and model weights are publicly available for further research and development at https://github.com/Alic-Li/BlackGoose_Rimer.

We present Visual AutoRegressive modeling (VAR), a new generation paradigm that redefines the autoregressive learning on images as coarse-to-fine "next-scale prediction" or "next-resolution prediction", diverging from the standard raster-scan "next-token prediction". This simple, intuitive methodology allows autoregressive (AR) transformers to learn visual distributions fast and generalize well: VAR, for the first time, makes AR models surpass diffusion transformers in image generation. On ImageNet 256x256 benchmark, VAR significantly improve AR baseline by improving Frechet inception distance (FID) from 18.65 to 1.80, inception score (IS) from 80.4 to 356.4, with around 20x faster inference speed. It is also empirically verified that VAR outperforms the Diffusion Transformer (DiT) in multiple dimensions including image quality, inference speed, data efficiency, and scalability. Scaling up VAR models exhibits clear power-law scaling laws similar to those observed in LLMs, with linear correlation coefficients near -0.998 as solid evidence. VAR further showcases zero-shot generalization ability in downstream tasks including image in-painting, out-painting, and editing. These results suggest VAR has initially emulated the two important properties of LLMs: Scaling Laws and zero-shot task generalization. We have released all models and codes to promote the exploration of AR/VAR models for visual generation and unified learning.

There exists recent work in computer vision, named VAR, that proposes a new autoregressive paradigm for image generation. Diverging from the vanilla next-token prediction, VAR structurally reformulates the image generation into a coarse to fine next-scale prediction. In this paper, we show that this scale-wise autoregressive framework can be effectively decoupled into intra-scale modeling, which captures local spatial dependencies within each scale, and inter-scale modeling, which models cross-scale relationships progressively from coarse-to-fine scales. This decoupling structure allows to rebuild VAR in a more computationally efficient manner. Specifically, for intra-scale modeling -- crucial for generating high-fidelity images -- we retain the original bidirectional self-attention design to ensure comprehensive modeling; for inter-scale modeling, which semantically connects different scales but is computationally intensive, we apply linear-complexity mechanisms like Mamba to substantially reduce computational overhead. We term this new framework M-VAR. Extensive experiments demonstrate that our method outperforms existing models in both image quality and generation speed. For example, our 1.5B model, with fewer parameters and faster inference speed, outperforms the largest VAR-d30-2B. Moreover, our largest model M-VAR-d32 impressively registers 1.78 FID on ImageNet 256times256 and outperforms the prior-art autoregressive models LlamaGen/VAR by 0.4/0.19 and popular diffusion models LDM/DiT by 1.82/0.49, respectively. Code is avaiable at https://github.com/OliverRensu/MVAR.

Recent advances in text-to-video (T2V) generation have enabled the creation of high-fidelity, temporally coherent clips from natural language prompts. Yet these systems come with significant computational costs, and their energy demands remain poorly understood. In this paper, we present a systematic study of the latency and energy consumption of state-of-the-art open-source T2V models. We first develop a compute-bound analytical model that predicts scaling laws with respect to spatial resolution, temporal length, and denoising steps. We then validate these predictions through fine-grained experiments on WAN2.1-T2V, showing quadratic growth with spatial and temporal dimensions, and linear scaling with the number of denoising steps. Finally, we extend our analysis to six diverse T2V models, comparing their runtime and energy profiles under default settings. Our results provide both a benchmark reference and practical insights for designing and deploying more sustainable generative video systems.

The population loss of trained deep neural networks often follows precise power-law scaling relations with either the size of the training dataset or the number of parameters in the network. We propose a theory that explains the origins of and connects these scaling laws. We identify variance-limited and resolution-limited scaling behavior for both dataset and model size, for a total of four scaling regimes. The variance-limited scaling follows simply from the existence of a well-behaved infinite data or infinite width limit, while the resolution-limited regime can be explained by positing that models are effectively resolving a smooth data manifold. In the large width limit, this can be equivalently obtained from the spectrum of certain kernels, and we present evidence that large width and large dataset resolution-limited scaling exponents are related by a duality. We exhibit all four scaling regimes in the controlled setting of large random feature and pretrained models and test the predictions empirically on a range of standard architectures and datasets. We also observe several empirical relationships between datasets and scaling exponents under modifications of task and architecture aspect ratio. Our work provides a taxonomy for classifying different scaling regimes, underscores that there can be different mechanisms driving improvements in loss, and lends insight into the microscopic origins of and relationships between scaling exponents.

Sequential VAEs have been successfully considered for many high-dimensional time series modelling problems, with many variant models relying on discrete-time mechanisms such as recurrent neural networks (RNNs). On the other hand, continuous-time methods have recently gained attraction, especially in the context of irregularly-sampled time series, where they can better handle the data than discrete-time methods. One such class are Gaussian process variational autoencoders (GPVAEs), where the VAE prior is set as a Gaussian process (GP). However, a major limitation of GPVAEs is that it inherits the cubic computational cost as GPs, making it unattractive to practioners. In this work, we leverage the equivalent discrete state space representation of Markovian GPs to enable linear time GPVAE training via Kalman filtering and smoothing. We show on a variety of high-dimensional temporal and spatiotemporal tasks that our method performs favourably compared to existing approaches whilst being computationally highly scalable.

Visual Autoregressive (VAR) modeling departs from the next-token prediction paradigm of traditional Autoregressive (AR) models through next-scale prediction, enabling high-quality image generation. However, the VAR paradigm suffers from sharply increased computational complexity and running time at large-scale steps. Although existing acceleration methods reduce runtime for large-scale steps, but rely on manual step selection and overlook the varying importance of different stages in the generation process. To address this challenge, we present StageVAR, a systematic study and stage-aware acceleration framework for VAR models. Our analysis shows that early steps are critical for preserving semantic and structural consistency and should remain intact, while later steps mainly refine details and can be pruned or approximated for acceleration. Building on these insights, StageVAR introduces a plug-and-play acceleration strategy that exploits semantic irrelevance and low-rank properties in late-stage computations, without requiring additional training. Our proposed StageVAR achieves up to 3.4x speedup with only a 0.01 drop on GenEval and a 0.26 decrease on DPG, consistently outperforming existing acceleration baselines. These results highlight stage-aware design as a powerful principle for efficient visual autoregressive image generation.

Visualizing multiple time series presents fundamental tradeoffs between scalability and visual clarity. Time series capture the behavior of many large-scale real-world processes, from stock market trends to urban activities. Users often gain insights by visualizing them as line charts, juxtaposing or superposing multiple time series to compare them and identify trends and patterns. However, existing representations struggle with scalability: when covering long time spans, leading to visual clutter from too many small multiples or overlapping lines. We propose TiVy, a new algorithm that summarizes time series using sequential patterns. It transforms the series into a set of symbolic sequences based on subsequence visual similarity using Dynamic Time Warping (DTW), then constructs a disjoint grouping of similar subsequences based on the frequent sequential patterns. The grouping result, a visual summary of time series, provides uncluttered superposition with fewer small multiples. Unlike common clustering techniques, TiVy extracts similar subsequences (of varying lengths) aligned in time. We also present an interactive time series visualization that renders large-scale time series in real-time. Our experimental evaluation shows that our algorithm (1) extracts clear and accurate patterns when visualizing time series data, (2) achieves a significant speed-up (1000X) compared to a straightforward DTW clustering. We also demonstrate the efficiency of our approach to explore hidden structures in massive time series data in two usage scenarios.

Visual Auto-Regressive (VAR) models significantly reduce inference steps through the "next-scale" prediction paradigm. However, progressive multi-scale generation incurs substantial memory overhead due to cumulative KV caching, limiting practical deployment. We observe a scale-depth asymmetric dependency in VAR: early scales exhibit extreme sensitivity to network depth, while later scales remain robust to depth reduction. Inspired by this, we propose VARiant: by equidistant sampling, we select multiple subnets ranging from 16 to 2 layers from the original 30-layer VAR-d30 network. Early scales are processed by the full network, while later scales utilize subnet. Subnet and the full network share weights, enabling flexible depth adjustment within a single model. However, weight sharing between subnet and the entire network can lead to optimization conflicts. To address this, we propose a progressive training strategy that breaks through the Pareto frontier of generation quality for both subnets and the full network under fixed-ratio training, achieving joint optimality. Experiments on ImageNet demonstrate that, compared to the pretrained VAR-d30 (FID 1.95), VARiant-d16 and VARiant-d8 achieve nearly equivalent quality (FID 2.05/2.12) while reducing memory consumption by 40-65%. VARiant-d2 achieves 3.5 times speedup and 80% memory reduction at moderate quality cost (FID 2.97). In terms of deployment, VARiant's single-model architecture supports zero-cost runtime depth switching and provides flexible deployment options from high quality to extreme efficiency, catering to diverse application scenarios.

Test-time scaling (TTS) has demonstrated remarkable success in enhancing large language models, yet its application to next-token prediction (NTP) autoregressive (AR) image generation remains largely uncharted. Existing TTS approaches for visual AR (VAR), which rely on frequent partial decoding and external reward models, are ill-suited for NTP-based image generation due to the inherent incompleteness of intermediate decoding results. To bridge this gap, we introduce ScalingAR, the first TTS framework specifically designed for NTP-based AR image generation that eliminates the need for early decoding or auxiliary rewards. ScalingAR leverages token entropy as a novel signal in visual token generation and operates at two complementary scaling levels: (i) Profile Level, which streams a calibrated confidence state by fusing intrinsic and conditional signals; and (ii) Policy Level, which utilizes this state to adaptively terminate low-confidence trajectories and dynamically schedule guidance for phase-appropriate conditioning strength. Experiments on both general and compositional benchmarks show that ScalingAR (1) improves base models by 12.5% on GenEval and 15.2% on TIIF-Bench, (2) efficiently reduces visual token consumption by 62.0% while outperforming baselines, and (3) successfully enhances robustness, mitigating performance drops by 26.0% in challenging scenarios.

Visual Auto-Regressive modeling (VAR) has shown promise in bridging the speed and quality gap between autoregressive image models and diffusion models. VAR reformulates autoregressive modeling by decomposing an image into successive resolution scales. During inference, an image is generated by predicting all the tokens in the next (higher-resolution) scale, conditioned on all tokens in all previous (lower-resolution) scales. However, this formulation suffers from reduced image quality due to the parallel generation of all tokens in a resolution scale; has sequence lengths scaling superlinearly in image resolution; and requires retraining to change the sampling schedule. We introduce Hierarchical Masked Auto-Regressive modeling (HMAR), a new image generation algorithm that alleviates these issues using next-scale prediction and masked prediction to generate high-quality images with fast sampling. HMAR reformulates next-scale prediction as a Markovian process, wherein the prediction of each resolution scale is conditioned only on tokens in its immediate predecessor instead of the tokens in all predecessor resolutions. When predicting a resolution scale, HMAR uses a controllable multi-step masked generation procedure to generate a subset of the tokens in each step. On ImageNet 256x256 and 512x512 benchmarks, HMAR models match or outperform parameter-matched VAR, diffusion, and autoregressive baselines. We develop efficient IO-aware block-sparse attention kernels that allow HMAR to achieve faster training and inference times over VAR by over 2.5x and 1.75x respectively, as well as over 3x lower inference memory footprint. Finally, HMAR yields additional flexibility over VAR; its sampling schedule can be changed without further training, and it can be applied to image editing tasks in a zero-shot manner.

In trajectory forecasting tasks for traffic, future output trajectories can be computed by advancing the ego vehicle's state with predicted actions according to a kinematics model. By unrolling predicted trajectories via time integration and models of kinematic dynamics, predicted trajectories should not only be kinematically feasible but also relate uncertainty from one timestep to the next. While current works in probabilistic prediction do incorporate kinematic priors for mean trajectory prediction, variance is often left as a learnable parameter, despite uncertainty in one time step being inextricably tied to uncertainty in the previous time step. In this paper, we show simple and differentiable analytical approximations describing the relationship between variance at one timestep and that at the next with the kinematic bicycle model. These approximations can be easily incorporated with negligible additional overhead into any existing trajectory forecasting framework utilizing probabilistic predictions, whether it is autoregressive or one-shot prediction. In our results, we find that encoding the relationship between variance across timesteps works especially well in unoptimal settings, such as with small or noisy datasets. We observe up to a 50% performance boost in partial dataset settings and up to an 8% performance boost in large-scale learning compared to previous kinematic prediction methods on SOTA trajectory forecasting architectures out-of-the-box, with no fine-tuning. In this paper, we show four analytical formulations of probabilistic kinematic priors which can be used for any Gaussian Mixture Model (GMM)-based deep learning models, quantify the error bound on linear approximations applied during trajectory unrolling, and show results to evaluate each formulation in trajectory forecasting.

As the marginal cost of scaling computation (data and parameters) during model pre-training continues to increase substantially, test-time scaling (TTS) has emerged as a promising direction for improving generative model performance by allocating additional computation at inference time. While TTS has demonstrated significant success across multiple language tasks, there remains a notable gap in understanding the test-time scaling behaviors of image and video generative models (diffusion-based or flow-based models). Although recent works have initiated exploration into inference-time strategies for vision tasks, these approaches face critical limitations: being constrained to task-specific domains, exhibiting poor scalability, or falling into reward over-optimization that sacrifices sample diversity. In this paper, we propose Evolutionary Search (EvoSearch), a novel, generalist, and efficient TTS method that effectively enhances the scalability of both image and video generation across diffusion and flow models, without requiring additional training or model expansion. EvoSearch reformulates test-time scaling for diffusion and flow models as an evolutionary search problem, leveraging principles from biological evolution to efficiently explore and refine the denoising trajectory. By incorporating carefully designed selection and mutation mechanisms tailored to the stochastic differential equation denoising process, EvoSearch iteratively generates higher-quality offspring while preserving population diversity. Through extensive evaluation across both diffusion and flow architectures for image and video generation tasks, we demonstrate that our method consistently outperforms existing approaches, achieves higher diversity, and shows strong generalizability to unseen evaluation metrics. Our project is available at the website https://tinnerhrhe.github.io/evosearch.

The new paradigm of test-time scaling has yielded remarkable breakthroughs in Large Language Models (LLMs) (e.g. reasoning models) and in generative vision models, allowing models to allocate additional computation during inference to effectively tackle increasingly complex problems. Despite the improvements of this approach, an important limitation emerges: the substantial increase in computation time makes the process slow and impractical for many applications. Given the success of this paradigm and its growing usage, we seek to preserve its benefits while eschewing the inference overhead. In this work we propose one solution to the critical problem of integrating test-time scaling knowledge into a model during post-training. Specifically, we replace reward guided test-time noise optimization in diffusion models with a Noise Hypernetwork that modulates initial input noise. We propose a theoretically grounded framework for learning this reward-tilted distribution for distilled generators, through a tractable noise-space objective that maintains fidelity to the base model while optimizing for desired characteristics. We show that our approach recovers a substantial portion of the quality gains from explicit test-time optimization at a fraction of the computational cost. Code is available at https://github.com/ExplainableML/HyperNoise

Test-time scaling has emerged as a prominent research direction in machine learning, enabling models to enhance their expressive capabilities during inference.Transformers, renowned for striking a delicate balance between efficiency and expressiveness, have benefited from test-time scaling techniques that leverage an expanding key-value (KV) cache to significantly improve performance.In this paper, we introduce a novel state-based approach to test-time scaling, which we term state tuning, tailored to the RNN-based RWKV-7 model.By exploiting the unique strengths of RWKV-7, our method achieves state-of-the-art performance on the target task without altering the model's pre-trained weights. Our approach centers on three key innovations. First, we develop an observer framework that allows a smaller model to replicate and learn the state dynamics of the RWKV-7 model. Second, we employ a kernel method to dynamically upscale the state size, enhancing the model's capacity to capture intricate patterns. Third, we integrate Decorrelated Backpropagation (DBP) to optimize the upscaled state matrix, thereby improving convergence and expressivity. By tuning only the state matrix, we demonstrate that a smaller model can outperform larger models on the given task. This method preserves the efficiency of the original RWKV-7 architecture while harnessing the power of test-time scaling to deliver superior results. Our findings underscore the potential of state tuning as an effective strategy for advancing model performance in resource-constrained settings. Our code is https://github.com/TorchRWKV/flash-linear-attention.

Large language models (LLMs) benefit from test-time scaling but are often hampered by high inference latency. Speculative decoding is a natural way to accelerate the scaling process; however, scaling along both the parallel and sequential dimensions poses significant challenges, including substantial memory-bound execution and synchronization overhead. We introduce ATTS (Asynchronous Test-Time Scaling), a statistically guaranteed adaptive scaling framework that follows the hypothesis testing process to address these challenges. By revisiting arithmetic intensity, ATTS identifies synchronization as the primary bottleneck. It enables asynchronous inference through online calibration and proposes an ordinal classification algorithm that supports a three-stage rejection sampling pipeline, scaling along both the sequential and parallel axes. Across experiments on the MATH, AMC23, AIME24, and AIME25 datasets and across multiple draft-target model families, we show that ATTS delivers up to 56.7x speedup in test-time scaling and a 4.14x throughput improvement, while maintaining accurate control of the rejection rate, reducing latency and memory overhead, and incurring no accuracy loss. By scaling both in parallel and sequential dimensions, we enable the 1.5B/70B draft/target model combination to achieve the performance of the state-of-the-art reasoning model o3-mini (high) on the AIME dataset. We have released the code at https://github.com/menik1126/asynchronous-test-time-scaling.

Test-time scaling is a powerful strategy for boosting the performance of large language models on complex reasoning tasks. While state-of-the-art approaches often employ generative verifiers to select the best solution from a pool of candidates, this method incurs prohibitive computational costs, limiting its practicality. In this work, we shift the focus to a more budget-aware paradigm: discriminative verification. We conduct a thorough empirical analysis and demonstrate that while discriminative verifiers may underperform in isolation, combining them with self-consistency in a hybrid approach creates a powerful and efficient test-time scaling mechanism. Notably, under a fixed compute budget, this hybrid approach surpasses state-of-the-art generative verification by a significant margin: achieving up to 15.3\% higher accuracy on AIME2025. Our findings establish that for practical, real-world applications, budget-aware scaling with discriminative verifiers is not only a "free" upgrade over self-consistency, but also a more effective and efficient alternative to costly generative techniques. Code is available at https://github.com/wang-research-lab/verification.

The Sequential Recommendation modeling paradigm is shifting from Transformer to Mamba architecture, which comprises two generations: Mamba1, based on the State Space Model (SSM), and Mamba2, based on State Space Duality (SSD). Although SSD offers superior computational efficiency compared to SSM, it suffers performance degradation in sequential recommendation tasks, especially in low-dimensional scenarios that are critical for these tasks. Considering that time-aware enhancement methods are commonly employed to mitigate performance loss, our analysis reveals that the performance decline of SSD can similarly be fundamentally compensated by leveraging mechanisms in time-aware methods. Thus, we propose integrating time-awareness into the SSD framework to address these performance issues. However, integrating current time-aware methods, modeled after TiSASRec, into SSD faces the following challenges: 1) the complexity of integrating these transformer-based mechanisms with the SSD architecture, and 2) the computational inefficiency caused by the need for dimensionality expansion of time-difference modeling. To overcome these challenges, we introduce a novel Time-aware Structured Masked Matrix that efficiently incorporates time-aware capabilities into SSD. Building on this, we propose Time-Aware Mamba for Recommendation (TiM4Rec), which mitigates performance degradation in low-dimensional SSD contexts while preserving computational efficiency. This marks the inaugural application of a time-aware enhancement method specifically tailored for the Mamba architecture within the domain of sequential recommendation. Extensive experiments conducted on three real-world datasets demonstrate the superiority of our approach. The code for our model is accessible at https://github.com/AlwaysFHao/TiM4Rec.

Training deep neural networks--and more recently, large models--demands efficient and scalable optimizers. Adaptive gradient algorithms like Adam, AdamW, and their variants have been central to this task. Despite the development of numerous variance reduction algorithms in the past decade aimed at accelerating stochastic optimization in both convex and nonconvex settings, variance reduction has not found widespread success in training deep neural networks or large language models. Consequently, it has remained a less favored approach in modern AI. In this paper, to unleash the power of variance reduction for efficient training of large models, we propose a unified optimization framework, MARS (Make vAriance Reduction Shine), which reconciles preconditioned gradient methods with variance reduction via a scaled stochastic recursive momentum technique. Within our framework, we introduce three instances of MARS that leverage preconditioned gradient updates based on AdamW, Lion, and Shampoo, respectively. We also draw a connection between our algorithms and existing optimizers. Experimental results on training GPT-2 models indicate that MARS consistently outperforms AdamW by a large margin.

World foundation models, which simulate the physical world by predicting future states from current observations and inputs, have become central to many applications in physical intelligence, including autonomous driving and robotics. However, these models require substantial computational resources for pretraining and are further constrained by available data during post-training. As such, scaling computation at test time emerges as both a critical and practical alternative to traditional model enlargement or re-training. In this work, we introduce SWIFT, a test-time scaling framework tailored for WFMs. SWIFT integrates our extensible WFM evaluation toolkit with process-level inference strategies, including fast tokenization, probability-based Top-K pruning, and efficient beam search. Empirical results on the COSMOS model demonstrate that test-time scaling exists even in a compute-optimal way. Our findings reveal that test-time scaling laws hold for WFMs and that SWIFT provides a scalable and effective pathway for improving WFM inference without retraining or increasing model size. The code is available at https://github.com/Mia-Cong/SWIFT.git.

Large multimodal reasoning models have achieved rapid progress, but their advancement is constrained by two major limitations: the absence of open, large-scale, high-quality long chain-of-thought (CoT) data, and the instability of reinforcement learning (RL) algorithms in post-training. Group Relative Policy Optimization (GRPO), the standard framework for RL fine-tuning, is prone to gradient vanishing when reward variance is low, which weakens optimization signals and impairs convergence. This work makes three contributions: (1) We propose Variance-Aware Sampling (VAS), a data selection strategy guided by Variance Promotion Score (VPS) that combines outcome variance and trajectory diversity to promote reward variance and stabilize policy optimization. (2) We release large-scale, carefully curated resources containing ~1.6M long CoT cold-start data and ~15k RL QA pairs, designed to ensure quality, difficulty, and diversity, along with a fully reproducible end-to-end training codebase. (3) We open-source a family of multimodal reasoning models in multiple scales, establishing standardized baselines for the community. Experiments across mathematical reasoning benchmarks demonstrate the effectiveness of both the curated data and the proposed VAS. Comprehensive ablation studies and analyses provide further insight into the contributions of each component. In addition, we theoretically establish that reward variance lower-bounds the expected policy gradient magnitude, with VAS serving as a practical mechanism to realize this guarantee. Our code, data, and checkpoints are available at https://github.com/LengSicong/MMR1.

We study variance-dependent regret bounds for Markov decision processes (MDPs). Algorithms with variance-dependent regret guarantees can automatically exploit environments with low variance (e.g., enjoying constant regret on deterministic MDPs). The existing algorithms are either variance-independent or suboptimal. We first propose two new environment norms to characterize the fine-grained variance properties of the environment. For model-based methods, we design a variant of the MVP algorithm (Zhang et al., 2021a). We apply new analysis techniques to demonstrate that this algorithm enjoys variance-dependent bounds with respect to the norms we propose. In particular, this bound is simultaneously minimax optimal for both stochastic and deterministic MDPs, the first result of its kind. We further initiate the study on model-free algorithms with variance-dependent regret bounds by designing a reference-function-based algorithm with a novel capped-doubling reference update schedule. Lastly, we also provide lower bounds to complement our upper bounds.

Invariance learning methods aim to learn invariant features in the hope that they generalize under distributional shifts. Although many tasks are naturally characterized by continuous domains, current invariance learning techniques generally assume categorically indexed domains. For example, auto-scaling in cloud computing often needs a CPU utilization prediction model that generalizes across different times (e.g., time of a day and date of a year), where `time' is a continuous domain index. In this paper, we start by theoretically showing that existing invariance learning methods can fail for continuous domain problems. Specifically, the naive solution of splitting continuous domains into discrete ones ignores the underlying relationship among domains, and therefore potentially leads to suboptimal performance. To address this challenge, we then propose Continuous Invariance Learning (CIL), which extracts invariant features across continuously indexed domains. CIL is a novel adversarial procedure that measures and controls the conditional independence between the labels and continuous domain indices given the extracted features. Our theoretical analysis demonstrates the superiority of CIL over existing invariance learning methods. Empirical results on both synthetic and real-world datasets (including data collected from production systems) show that CIL consistently outperforms strong baselines among all the tasks.

Test-time compute scaling has emerged as a new axis along which to improve model accuracy, where additional computation is used at inference time to allow the model to think longer for more challenging problems. One promising approach for test-time compute scaling is search against a process reward model, where a model generates multiple potential candidates at each step of the search, and these partial trajectories are then scored by a separate reward model in order to guide the search process. The diversity of trajectories in the tree search process affects the accuracy of the search, since increasing diversity promotes more exploration. However, this diversity comes at a cost, as divergent trajectories have less KV sharing, which means they consume more memory and slow down the search process. Previous search methods either do not perform sufficient exploration, or else explore diverse trajectories but have high latency. We address this challenge by proposing Efficient Tree Search (ETS), which promotes KV sharing by pruning redundant trajectories while maintaining necessary diverse trajectories. ETS incorporates a linear programming cost model to promote KV cache sharing by penalizing the number of nodes retained, while incorporating a semantic coverage term into the cost model to ensure that we retain trajectories which are semantically different. We demonstrate how ETS can achieve 1.8times reduction in average KV cache size during the search process, leading to 1.4times increased throughput relative to prior state-of-the-art methods, with minimal accuracy degradation and without requiring any custom kernel implementation. Code is available at: https://github.com/SqueezeAILab/ETS.

Scale has become a main ingredient in obtaining strong machine learning models. As a result, understanding a model's scaling properties is key to effectively designing both the right training setup as well as future generations of architectures. In this work, we argue that scale and training research has been needlessly complex due to reliance on the cosine schedule, which prevents training across different lengths for the same model size. We investigate the training behavior of a direct alternative - constant learning rate and cooldowns - and find that it scales predictably and reliably similar to cosine. Additionally, we show that stochastic weight averaging yields improved performance along the training trajectory, without additional training costs, across different scales. Importantly, with these findings we demonstrate that scaling experiments can be performed with significantly reduced compute and GPU hours by utilizing fewer but reusable training runs.

Scaling laws offer valuable insights into the design of time series foundation models (TSFMs). However, previous research has largely focused on the scaling laws of TSFMs for in-distribution (ID) data, leaving their out-of-distribution (OOD) scaling behavior and the influence of model architectures less explored. In this work, we examine two common TSFM architectures, encoder-only and decoder-only Transformers, and investigate their scaling behavior on both ID and OOD data. These models are trained and evaluated across varying parameter counts, compute budgets, and dataset sizes. Our experiments reveal that the log-likelihood loss of TSFMs exhibits similar scaling behavior in both OOD and ID settings. We further compare the scaling properties across different architectures, incorporating two state-of-the-art TSFMs as case studies, showing that model architecture plays a significant role in scaling. The encoder-only Transformers demonstrate better scalability than the decoder-only Transformers, while the architectural enhancements in the two advanced TSFMs primarily improve ID performance but reduce OOD scalability. While scaling up TSFMs is expected to drive performance breakthroughs, the lack of a comprehensive understanding of TSFM scaling laws has hindered the development of a robust framework to guide model scaling. We fill this gap in this work by synthesizing our findings and providing practical guidelines for designing and scaling larger TSFMs with enhanced model capabilities.

Data balancing across multiple modalities and sources appears in various forms in foundation models in machine learning and AI, e.g. in CLIP and DINO. We show that data balancing across modalities and sources actually offers an unsuspected benefit: variance reduction. We present a non-asymptotic statistical bound that quantifies this variance reduction effect and relates it to the eigenvalue decay of Markov operators. Furthermore, we describe how various forms of data balancing in contrastive multimodal learning and self-supervised clustering can be better understood, and even improved upon, owing to our variance reduction viewpoint.

Generating minute-long videos is a critical step toward developing world models, providing a foundation for realistic extended scenes and advanced AI simulators. The emerging semi-autoregressive (block diffusion) paradigm integrates the strengths of diffusion and autoregressive models, enabling arbitrary-length video generation and improving inference efficiency through KV caching and parallel sampling. However, it yet faces two enduring challenges: (i) KV-cache-induced long-horizon error accumulation, and (ii) the lack of fine-grained long-video benchmarks and coherence-aware metrics. To overcome these limitations, we propose BlockVid, a novel block diffusion framework equipped with semantic-aware sparse KV cache, an effective training strategy called Block Forcing, and dedicated chunk-wise noise scheduling and shuffling to reduce error propagation and enhance temporal consistency. We further introduce LV-Bench, a fine-grained benchmark for minute-long videos, complete with new metrics evaluating long-range coherence. Extensive experiments on VBench and LV-Bench demonstrate that BlockVid consistently outperforms existing methods in generating high-quality, coherent minute-long videos. In particular, it achieves a 22.2% improvement on VDE Subject and a 19.4% improvement on VDE Clarity in LV-Bench over the state of the art approaches. Project website: https://ziplab.co/BlockVid. Inferix (Code): https://github.com/alibaba-damo-academy/Inferix.

We study contextual combinatorial bandits with probabilistically triggered arms (C^2MAB-T) under a variety of smoothness conditions that capture a wide range of applications, such as contextual cascading bandits and contextual influence maximization bandits. Under the triggering probability modulated (TPM) condition, we devise the C^2-UCB-T algorithm and propose a novel analysis that achieves an O(dKT) regret bound, removing a potentially exponentially large factor O(1/p_{min}), where d is the dimension of contexts, p_{min} is the minimum positive probability that any arm can be triggered, and batch-size K is the maximum number of arms that can be triggered per round. Under the variance modulated (VM) or triggering probability and variance modulated (TPVM) conditions, we propose a new variance-adaptive algorithm VAC^2-UCB and derive a regret bound O(dT), which is independent of the batch-size K. As a valuable by-product, our analysis technique and variance-adaptive algorithm can be applied to the CMAB-T and C^2MAB setting, improving existing results there as well. We also include experiments that demonstrate the improved performance of our algorithms compared with benchmark algorithms on synthetic and real-world datasets.

Fast and scalable alignment of time series is a fundamental challenge in many domains. The standard solution, Dynamic Time Warping (DTW), struggles with poor scalability and sensitivity to noise. We introduce TimePoint, a self-supervised method that dramatically accelerates DTW-based alignment while typically improving alignment accuracy by learning keypoints and descriptors from synthetic data. Inspired by 2D keypoint detection but carefully adapted to the unique challenges of 1D signals, TimePoint leverages efficient 1D diffeomorphisms, which effectively model nonlinear time warping, to generate realistic training data. This approach, along with fully convolutional and wavelet convolutional architectures, enables the extraction of informative keypoints and descriptors. Applying DTW to these sparse representations yield major speedups and typically higher alignment accuracy than standard DTW applied to the full signals. TimePoint demonstrates strong generalization to real-world time series when trained solely on synthetic data, and further improves with fine-tuning on real data. Extensive experiments demonstrate that TimePoint consistently achieves faster and more accurate alignments than standard DTW, making it a scalable solution for time-series analysis. Our code is available at https://github.com/BGU-CS-VIL/TimePoint

Autoregressive models, despite their commendable performance in a myriad of generative tasks, face challenges stemming from their inherently sequential structure. Inference on these models, by design, harnesses a temporal dependency, where the current token's probability distribution is conditioned on preceding tokens. This inherent characteristic severely impedes computational efficiency during inference as a typical inference request can require more than thousands of tokens, where generating each token requires a load of entire model weights, making the inference more memory-bound. The large overhead becomes profound in real deployment where requests arrive randomly, necessitating various generation lengths. Existing solutions, such as dynamic batching and concurrent instances, introduce significant response delays and bandwidth contention, falling short of achieving optimal latency and throughput. To address these shortcomings, we propose Flover -- a temporal fusion framework for efficiently inferring multiple requests in parallel. We deconstruct the general generation pipeline into pre-processing and token generation, and equip the framework with a dedicated work scheduler for fusing the generation process temporally across all requests. By orchestrating the token-level parallelism, Flover exhibits optimal hardware efficiency and significantly spares the system resources. By further employing a fast buffer reordering algorithm that allows memory eviction of finished tasks, it brings over 11x inference speedup on GPT and 16x on LLAMA compared to the cutting-edge solutions provided by NVIDIA FasterTransformer. Crucially, by leveraging the advanced tensor parallel technique, Flover proves efficacious across diverse computational landscapes, from single-GPU setups to distributed scenarios, thereby offering robust performance optimization that adapts to variable use cases.

With the rapid deployment of SCADA systems, how to effectively analyze industrial signals and detect abnormal states is an urgent need for the industry. Due to the significant heterogeneity of these signals, which we summarize as the M5 problem, previous works only focus on small sub-problems and employ specialized models, failing to utilize the synergies between modalities and the powerful scaling law. However, we argue that the M5 signals can be modeled in a unified manner due to the intrinsic similarity. As a result, we propose FISHER, a Foundation model for multi-modal Industrial Signal compreHEnsive Representation. To support arbitrary sampling rates, FISHER considers the increment of sampling rate as the concatenation of sub-band information. Specifically, FISHER takes the STFT sub-band as the modeling unit and adopts a teacher student SSL framework for pre-training. We also develop the RMIS benchmark, which evaluates the representations of M5 industrial signals on multiple health management tasks. Compared with top SSL models, FISHER showcases versatile and outstanding capabilities with a general performance gain up to 5.03%, along with much more efficient scaling curves. We also investigate the scaling law on downstream tasks and derive potential avenues for future works. FISHER is now open-sourced on https://github.com/jianganbai/FISHER

We introduce MOMENT, a family of open-source foundation models for general-purpose time-series analysis. Pre-training large models on time-series data is challenging due to (1) the absence of a large and cohesive public time-series repository, and (2) diverse time-series characteristics which make multi-dataset training onerous. Additionally, (3) experimental benchmarks to evaluate these models, especially in scenarios with limited resources, time, and supervision, are still in their nascent stages. To address these challenges, we compile a large and diverse collection of public time-series, called the Time-series Pile, and systematically tackle time-series-specific challenges to unlock large-scale multi-dataset pre-training. Finally, we build on recent work to design a benchmark to evaluate time-series foundation models on diverse tasks and datasets in limited supervision settings. Experiments on this benchmark demonstrate the effectiveness of our pre-trained models with minimal data and task-specific fine-tuning. Finally, we present several interesting empirical observations about large pre-trained time-series models. Our code is available anonymously at anonymous.4open.science/r/BETT-773F/.

Text-to-image generation with visual autoregressive~(VAR) models has recently achieved impressive advances in generation fidelity and inference efficiency. While control mechanisms have been explored for diffusion models, enabling precise and flexible control within VAR paradigm remains underexplored. To bridge this critical gap, in this paper, we introduce ScaleWeaver, a novel framework designed to achieve high-fidelity, controllable generation upon advanced VAR models through parameter-efficient fine-tuning. The core module in ScaleWeaver is the improved MMDiT block with the proposed Reference Attention module, which efficiently and effectively incorporates conditional information. Different from MM Attention, the proposed Reference Attention module discards the unnecessary attention from imagerightarrowcondition, reducing computational cost while stabilizing control injection. Besides, it strategically emphasizes parameter reuse, leveraging the capability of the VAR backbone itself with a few introduced parameters to process control information, and equipping a zero-initialized linear projection to ensure that control signals are incorporated effectively without disrupting the generative capability of the base model. Extensive experiments show that ScaleWeaver delivers high-quality generation and precise control while attaining superior efficiency over diffusion-based methods, making ScaleWeaver a practical and effective solution for controllable text-to-image generation within the visual autoregressive paradigm. Code and models will be released.

Test-Time Scaling (TTS) has proven effective in improving the performance of Large Language Models (LLMs) during inference. However, existing research has overlooked the efficiency of TTS from a latency-sensitive perspective. Through a latency-aware evaluation of representative TTS methods, we demonstrate that a compute-optimal TTS does not always result in the lowest latency in scenarios where latency is critical. To address this gap and achieve latency-optimal TTS, we propose two key approaches by optimizing the concurrency configurations: (1) branch-wise parallelism, which leverages multiple concurrent inference branches, and (2) sequence-wise parallelism, enabled by speculative decoding. By integrating these two approaches and allocating computational resources properly to each, our latency-optimal TTS enables a 32B model to reach 82.3% accuracy on MATH-500 within 1 minute and a smaller 3B model to achieve 72.4% within 10 seconds. Our work emphasizes the importance of latency-aware TTS and demonstrates its ability to deliver both speed and accuracy in latency-sensitive scenarios.

We study inference-time scaling for diffusion models, where the goal is to adapt a pre-trained model to new target distributions without retraining. Existing guidance-based methods are simple but introduce bias, while particle-based corrections suffer from weight degeneracy and high computational cost. We introduce DriftLite, a lightweight, training-free particle-based approach that steers the inference dynamics on the fly with provably optimal stability control. DriftLite exploits a previously unexplored degree of freedom in the Fokker-Planck equation between the drift and particle potential, and yields two practical instantiations: Variance- and Energy-Controlling Guidance (VCG/ECG) for approximating the optimal drift with minimal overhead. Across Gaussian mixture models, particle systems, and large-scale protein-ligand co-folding problems, DriftLite consistently reduces variance and improves sample quality over pure guidance and sequential Monte Carlo baselines. These results highlight a principled, efficient route toward scalable inference-time adaptation of diffusion models.

Generating temporal data under conditions is crucial for forecasting, imputation, and generative tasks. Such data often has metadata and partially observed signals that jointly influence the generated values. However, existing methods face three key limitations: (1) they condition on either the metadata or observed values, but rarely both together; (2) they adopt either training-time approaches that fail to generalize to unseen scenarios, or inference-time approaches that ignore metadata; and (3) they suffer from trade-offs between generation speed and temporal coherence across time windows--choosing either slow but coherent autoregressive methods or fast but incoherent parallel ones. We propose WaveStitch, a novel diffusion-based method to overcome these hurdles through: (1) dual-sourced conditioning on both metadata and partially observed signals; (2) a hybrid training-inference architecture, incorporating metadata during training and observations at inference via gradient-based guidance; and (3) a novel pipeline-style paradigm that generates time windows in parallel while preserving coherence through an inference-time conditional loss and a stitching mechanism. Across diverse datasets, WaveStitch demonstrates adaptability to arbitrary patterns of observed signals, achieving 1.81x lower mean-squared-error compared to the state-of-the-art, and generates data up to 166.48x faster than autoregressive methods while maintaining coherence. Our code is available at: https://github.com/adis98/WaveStitch

Activation functions are fundamental in deep neural networks and directly impact gradient flow, optimization stability, and generalization. Although ReLU remains standard because of its simplicity, it suffers from vanishing gradients and lacks adaptability. Alternatives like Swish and GELU introduce smooth transitions, but fail to dynamically adjust to input statistics. We propose VeLU, a Variance-enhanced Learning Unit as an activation function that dynamically scales based on input variance by integrating ArcTan-Sin transformations and Wasserstein-2 regularization, effectively mitigating covariate shifts and stabilizing optimization. Extensive experiments on ViT_B16, VGG19, ResNet50, DenseNet121, MobileNetV2, and EfficientNetB3 confirm VeLU's superiority over ReLU, ReLU6, Swish, and GELU on six vision benchmarks. The codes of VeLU are publicly available on GitHub.

Existing acceleration techniques for video diffusion models often rely on uniform heuristics or time-embedding variants to skip timesteps and reuse cached features. These approaches typically require extensive calibration with curated prompts and risk inconsistent outputs due to prompt-specific overfitting. In this paper, we introduce a novel and robust discovery: a unified magnitude law observed across different models and prompts. Specifically, the magnitude ratio of successive residual outputs decreases monotonically and steadily in most timesteps while rapidly in the last several steps. Leveraging this insight, we introduce a Magnitude-aware Cache (MagCache) that adaptively skips unimportant timesteps using an error modeling mechanism and adaptive caching strategy. Unlike existing methods requiring dozens of curated samples for calibration, MagCache only requires a single sample for calibration. Experimental results show that MagCache achieves 2.1x and 2.68x speedups on Open-Sora and Wan 2.1, respectively, while preserving superior visual fidelity. It significantly outperforms existing methods in LPIPS, SSIM, and PSNR, under comparable computational budgets.

With the scale capability of increasing training data, model size, and computational cost, video generation has achieved impressive results in digital creation, enabling users to express creativity across various domains. Recently, researchers in Large Language Models (LLMs) have expanded the scaling to test-time, which can significantly improve LLM performance by using more inference-time computation. Instead of scaling up video foundation models through expensive training costs, we explore the power of Test-Time Scaling (TTS) in video generation, aiming to answer the question: if a video generation model is allowed to use non-trivial amount of inference-time compute, how much can it improve generation quality given a challenging text prompt. In this work, we reinterpret the test-time scaling of video generation as a searching problem to sample better trajectories from Gaussian noise space to the target video distribution. Specifically, we build the search space with test-time verifiers to provide feedback and heuristic algorithms to guide searching process. Given a text prompt, we first explore an intuitive linear search strategy by increasing noise candidates at inference time. As full-step denoising all frames simultaneously requires heavy test-time computation costs, we further design a more efficient TTS method for video generation called Tree-of-Frames (ToF) that adaptively expands and prunes video branches in an autoregressive manner. Extensive experiments on text-conditioned video generation benchmarks demonstrate that increasing test-time compute consistently leads to significant improvements in the quality of videos. Project page: https://liuff19.github.io/Video-T1

User preferences follow a dynamic pattern over a day, e.g., at 8 am, a user might prefer to read news, while at 8 pm, they might prefer to watch movies. Time modeling aims to enable recommendation systems to perceive time changes to capture users' dynamic preferences over time, which is an important and challenging problem in recommendation systems. Especially, streaming recommendation systems in the industry, with only available samples of the current moment, present greater challenges for time modeling. There is still a lack of effective time modeling methods for streaming recommendation systems. In this paper, we propose an effective and universal method Interest Clock to perceive time information in recommendation systems. Interest Clock first encodes users' time-aware preferences into a clock (hour-level personalized features) and then uses Gaussian distribution to smooth and aggregate them into the final interest clock embedding according to the current time for the final prediction. By arming base models with Interest Clock, we conduct online A/B tests, obtaining +0.509% and +0.758% improvements on user active days and app duration respectively. Besides, the extended offline experiments show improvements as well. Interest Clock has been deployed on Douyin Music App.

Time series foundation models have shown impressive performance on a variety of tasks, across a wide range of domains, even in zero-shot settings. However, most of these models are designed to handle short univariate time series as an input. This limits their practical use, especially in domains such as healthcare with copious amounts of long and multivariate data with strong temporal and intra-variate dependencies. Our study bridges this gap by cataloging and systematically comparing various context expansion techniques from both language and time series domains, and introducing a novel compressive memory mechanism to allow encoder-only TSFMs to effectively model intra-variate dependencies. We demonstrate the benefits of our approach by imbuing MOMENT, a recent family of multi-task time series foundation models, with the multivariate context.

Typical neural network trainings have substantial variance in test-set performance between repeated runs, impeding hyperparameter comparison and training reproducibility. We present the following results towards understanding this variation. (1) Despite having significant variance on their test-sets, we demonstrate that standard CIFAR-10 and ImageNet trainings have very little variance in their performance on the test-distributions from which those test-sets are sampled, suggesting that variance is less of a practical issue than previously thought. (2) We present a simplifying statistical assumption which closely approximates the structure of the test-set accuracy distribution. (3) We argue that test-set variance is inevitable in the following two senses. First, we show that variance is largely caused by high sensitivity of the training process to initial conditions, rather than by specific sources of randomness like the data order and augmentations. Second, we prove that variance is unavoidable given the observation that ensembles of trained networks are well-calibrated. (4) We conduct preliminary studies of distribution-shift, fine-tuning, data augmentation and learning rate through the lens of variance between runs.

A prominent approach to test-time scaling for text-to-image diffusion models formulates the problem as a search over multiple noise seeds, selecting the one that maximizes a certain image-reward function. The effectiveness of this strategy heavily depends on the number and diversity of noise seeds explored. However, verifying each candidate is computationally expensive, because each must be fully denoised before a reward can be computed. This severely limits the number of samples that can be explored under a fixed budget. We propose test-time scaling with noise-aware pruning (TTSnap), a framework that prunes low-quality candidates without fully denoising them. The key challenge is that reward models are learned in the clean image domain, and the ranking of rewards predicted for intermediate estimates are often inconsistent with those predicted for clean images. To overcome this, we train noise-aware reward models via self-distillation to align the reward for intermediate estimates with that of the final clean images. To stabilize learning across different noise levels, we adopt a curriculum training strategy that progressively shifts the data domain from clean images to noise images. In addition, we introduce a new metric that measures reward alignment and computational budget utilization. Experiments demonstrate that our approach improves performance by over 16\% compared with existing methods, enabling more efficient and effective test-time scaling. It also provides orthogonal gains when combined with post-training techniques and local test-time optimization. Code: https://github.com/TerrysLearning/TTSnap/.

As enthusiasm for scaling computation (data and parameters) in the pretraining era gradually diminished, test-time scaling (TTS), also referred to as ``test-time computing'' has emerged as a prominent research focus. Recent studies demonstrate that TTS can further elicit the problem-solving capabilities of large language models (LLMs), enabling significant breakthroughs not only in specialized reasoning tasks, such as mathematics and coding, but also in general tasks like open-ended Q&A. However, despite the explosion of recent efforts in this area, there remains an urgent need for a comprehensive survey offering a systemic understanding. To fill this gap, we propose a unified, multidimensional framework structured along four core dimensions of TTS research: what to scale, how to scale, where to scale, and how well to scale. Building upon this taxonomy, we conduct an extensive review of methods, application scenarios, and assessment aspects, and present an organized decomposition that highlights the unique functional roles of individual techniques within the broader TTS landscape. From this analysis, we distill the major developmental trajectories of TTS to date and offer hands-on guidelines for practical deployment. Furthermore, we identify several open challenges and offer insights into promising future directions, including further scaling, clarifying the functional essence of techniques, generalizing to more tasks, and more attributions.

This paper explores Large Batch Training techniques using layer-wise adaptive scaling ratio (LARS) across diverse settings, uncovering insights. LARS algorithms with warm-up tend to be trapped in sharp minimizers early on due to redundant ratio scaling. Additionally, a fixed steep decline in the latter phase restricts deep neural networks from effectively navigating early-phase sharp minimizers. Building on these findings, we propose Time Varying LARS (TVLARS), a novel algorithm that replaces warm-up with a configurable sigmoid-like function for robust training in the initial phase. TVLARS promotes gradient exploration early on, surpassing sharp optimizers and gradually transitioning to LARS for robustness in later phases. Extensive experiments demonstrate that TVLARS consistently outperforms LARS and LAMB in most cases, with up to 2\% improvement in classification scenarios. Notably, in all self-supervised learning cases, TVLARS dominates LARS and LAMB with performance improvements of up to 10\%.

Autoregressive (AR) transformers have emerged as a powerful paradigm for visual generation, largely due to their scalability, computational efficiency and unified architecture with language and vision. Among them, next scale prediction Visual Autoregressive Generation (VAR) has recently demonstrated remarkable performance, even surpassing diffusion-based models. In this work, we revisit VAR and uncover a theoretical insight: when equipped with a Markovian attention mask, VAR is mathematically equivalent to a discrete diffusion. We term this reinterpretation as Scalable Visual Refinement with Discrete Diffusion (SRDD), establishing a principled bridge between AR transformers and diffusion models. Leveraging this new perspective, we show how one can directly import the advantages of diffusion such as iterative refinement and reduce architectural inefficiencies into VAR, yielding faster convergence, lower inference cost, and improved zero-shot reconstruction. Across multiple datasets, we show that the diffusion based perspective of VAR leads to consistent gains in efficiency and generation.

Generative models trained on extensive high-quality datasets effectively capture the structural and statistical properties of clean images, rendering them powerful priors for transforming degraded features into clean ones in image restoration. VAR, a novel image generative paradigm, surpasses diffusion models in generation quality by applying a next-scale prediction approach. It progressively captures both global structures and fine-grained details through the autoregressive process, consistent with the multi-scale restoration principle widely acknowledged in the restoration community. Furthermore, we observe that during the image reconstruction process utilizing VAR, scale predictions automatically modulate the input, facilitating the alignment of representations at subsequent scales with the distribution of clean images. To harness VAR's adaptive distribution alignment capability in image restoration tasks, we formulate the multi-scale latent representations within VAR as the restoration prior, thus advancing our delicately designed VarFormer framework. The strategic application of these priors enables our VarFormer to achieve remarkable generalization on unseen tasks while also reducing training computational costs. Extensive experiments underscores that our VarFormer outperforms existing multi-task image restoration methods across various restoration tasks.

Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical difficulties of estimating time-varying and high-dimensional covariance matrices often limits existing methods to handling at most a few hundred dimensions or requires making strong assumptions on the dependence between series. We propose to combine an RNN-based time series model with a Gaussian copula process output model with a low-rank covariance structure to reduce the computational complexity and handle non-Gaussian marginal distributions. This permits to drastically reduce the number of parameters and consequently allows the modeling of time-varying correlations of thousands of time series. We show on several real-world datasets that our method provides significant accuracy improvements over state-of-the-art baselines and perform an ablation study analyzing the contributions of the different components of our model.

One common strategy for improving the performance of Large Language Models (LLMs) on downstream tasks involves using a verifier model to either select the best answer from a pool of candidates or to steer the auto-regressive generation process towards better outputs. This class of methods typically results in improved accuracy at the cost of increased computation at test-time, a paradigm known as test-time scaling. However, most existing approaches increase computation uniformly across all samples and generation steps, without considering the complexity of individual instances, leading to inefficient resource use. We address this limitation by proposing an approach, called Locally Adaptive Test-Time Scaling (LATTS), that allocates variable compute across generation steps. Specifically, at each generation step, LATTS employs a verifier-based acceptance criterion to decide whether to resample, backtrack, restart, or stop the generation process. This criterion effectively adjusts the per-step computational effort based on a precise notion of local difficulty derived from the verifier model. Empirical results show that LATTS achieves significantly superior accuracy--compute tradeoffs compared to standard verifier-based methods.

The recovery of time-varying graph signals is a fundamental problem with numerous applications in sensor networks and forecasting in time series. Effectively capturing the spatio-temporal information in these signals is essential for the downstream tasks. Previous studies have used the smoothness of the temporal differences of such graph signals as an initial assumption. Nevertheless, this smoothness assumption could result in a degradation of performance in the corresponding application when the prior does not hold. In this work, we relax the requirement of this hypothesis by including a learning module. We propose a Time Graph Neural Network (TimeGNN) for the recovery of time-varying graph signals. Our algorithm uses an encoder-decoder architecture with a specialized loss composed of a mean squared error function and a Sobolev smoothness operator.TimeGNN shows competitive performance against previous methods in real datasets.

Deep learning for time series forecasting has seen significant advancements over the past decades. However, despite the success of large-scale pre-training in language and vision domains, pre-trained time series models remain limited in scale and operate at a high cost, hindering the development of larger capable forecasting models in real-world applications. In response, we introduce Time-MoE, a scalable and unified architecture designed to pre-train larger, more capable forecasting foundation models while reducing inference costs. By leveraging a sparse mixture-of-experts (MoE) design, Time-MoE enhances computational efficiency by activating only a subset of networks for each prediction, reducing computational load while maintaining high model capacity. This allows Time-MoE to scale effectively without a corresponding increase in inference costs. Time-MoE comprises a family of decoder-only transformer models that operate in an auto-regressive manner and support flexible forecasting horizons with varying input context lengths. We pre-trained these models on our newly introduced large-scale data Time-300B, which spans over 9 domains and encompassing over 300 billion time points. For the first time, we scaled a time series foundation model up to 2.4 billion parameters, achieving significantly improved forecasting precision. Our results validate the applicability of scaling laws for training tokens and model size in the context of time series forecasting. Compared to dense models with the same number of activated parameters or equivalent computation budgets, our models consistently outperform them by large margin. These advancements position Time-MoE as a state-of-the-art solution for tackling real-world time series forecasting challenges with superior capability, efficiency, and flexibility.

Diffusion models have revolutionized image generation, and their extension to video generation has shown promise. However, current video diffusion models~(VDMs) rely on a scalar timestep variable applied at the clip level, which limits their ability to model complex temporal dependencies needed for various tasks like image-to-video generation. To address this limitation, we propose a frame-aware video diffusion model~(FVDM), which introduces a novel vectorized timestep variable~(VTV). Unlike conventional VDMs, our approach allows each frame to follow an independent noise schedule, enhancing the model's capacity to capture fine-grained temporal dependencies. FVDM's flexibility is demonstrated across multiple tasks, including standard video generation, image-to-video generation, video interpolation, and long video synthesis. Through a diverse set of VTV configurations, we achieve superior quality in generated videos, overcoming challenges such as catastrophic forgetting during fine-tuning and limited generalizability in zero-shot methods.Our empirical evaluations show that FVDM outperforms state-of-the-art methods in video generation quality, while also excelling in extended tasks. By addressing fundamental shortcomings in existing VDMs, FVDM sets a new paradigm in video synthesis, offering a robust framework with significant implications for generative modeling and multimedia applications.

Diffusion models have been widely adopted in image and video generation. However, their complex network architecture leads to high inference overhead for its generation process. Existing diffusion quantization methods primarily focus on the quantization of the model structure while ignoring the impact of time-steps variation during sampling. At the same time, most current approaches fail to account for significant activations that cannot be eliminated, resulting in substantial performance degradation after quantization. To address these issues, we propose Time-Rotation Diffusion Quantization (TR-DQ), a novel quantization method incorporating time-step and rotation-based optimization. TR-DQ first divides the sampling process based on time-steps and applies a rotation matrix to smooth activations and weights dynamically. For different time-steps, a dedicated hyperparameter is introduced for adaptive timing modeling, which enables dynamic quantization across different time steps. Additionally, we also explore the compression potential of Classifier-Free Guidance (CFG-wise) to establish a foundation for subsequent work. TR-DQ achieves state-of-the-art (SOTA) performance on image generation and video generation tasks and a 1.38-1.89x speedup and 1.97-2.58x memory reduction in inference compared to existing quantization methods.

Test-time scaling has emerged as a transformative paradigm for enhancing the performance of large reasoning models, enabling dynamic allocation of computational resources during inference. However, as the landscape of reasoning models rapidly expands, a critical question remains: how can we systematically compare and evaluate the test-time scaling capabilities across different models? In this paper, we introduce ARISE (Adaptive Resolution-aware Scaling Evaluation), a novel metric specifically designed to assess the test-time scaling effectiveness of large reasoning models. Unlike existing evaluation approaches, ARISE incorporates two key innovations: (1) sample-level awareness that effectively penalizes negative scaling behaviors where increased computation leads to performance degradation, and (2) a dynamic sampling mechanism that mitigates the impact of accuracy fluctuations and token count instability on the final assessment. We conduct comprehensive experiments evaluating state-of-the-art reasoning models across diverse domains including mathematical reasoning, code generation, and agentic tasks. Our results demonstrate that ARISE provides a reliable and fine-grained measurement of test-time scaling capabilities, revealing significant variations in scaling efficiency across models. Notably, our evaluation identifies Claude Opus as exhibiting superior scaling characteristics compared to other contemporary reasoning models.

Mirror descent value iteration (MDVI), an abstraction of Kullback-Leibler (KL) and entropy-regularized reinforcement learning (RL), has served as the basis for recent high-performing practical RL algorithms. However, despite the use of function approximation in practice, the theoretical understanding of MDVI has been limited to tabular Markov decision processes (MDPs). We study MDVI with linear function approximation through its sample complexity required to identify an varepsilon-optimal policy with probability 1-delta under the settings of an infinite-horizon linear MDP, generative model, and G-optimal design. We demonstrate that least-squares regression weighted by the variance of an estimated optimal value function of the next state is crucial to achieving minimax optimality. Based on this observation, we present Variance-Weighted Least-Squares MDVI (VWLS-MDVI), the first theoretical algorithm that achieves nearly minimax optimal sample complexity for infinite-horizon linear MDPs. Furthermore, we propose a practical VWLS algorithm for value-based deep RL, Deep Variance Weighting (DVW). Our experiments demonstrate that DVW improves the performance of popular value-based deep RL algorithms on a set of MinAtar benchmarks.

Diffusion models have achieved remarkable success as generative models. However, even a well-trained model can accumulate errors throughout the generation process. These errors become particularly problematic when arbitrary guidance is applied to steer samples toward desired properties, which often breaks sample fidelity. In this paper, we propose a general solution to address the off-manifold phenomenon observed in diffusion models. Our approach leverages a time predictor to estimate deviations from the desired data manifold at each timestep, identifying that a larger time gap is associated with reduced generation quality. We then design a novel guidance mechanism, `Temporal Alignment Guidance' (TAG), attracting the samples back to the desired manifold at every timestep during generation. Through extensive experiments, we demonstrate that TAG consistently produces samples closely aligned with the desired manifold at each timestep, leading to significant improvements in generation quality across various downstream tasks.

Most bandit algorithms assume that the reward variances or their upper bounds are known, and that they are the same for all arms. This naturally leads to suboptimal performance and higher regret due to variance overestimation. On the other hand, underestimated reward variances may lead to linear regret due to committing early to a suboptimal arm. This motivated prior works on variance-adaptive frequentist algorithms, which have strong instance-dependent regret bounds but cannot incorporate prior knowledge on reward variances. We lay foundations for the Bayesian setting, which incorporates prior knowledge. This results in lower regret in practice, due to using the prior in the algorithm design, and also improved regret guarantees. Specifically, we study Gaussian bandits with {unknown heterogeneous reward variances}, and develop a Thompson sampling algorithm with prior-dependent Bayes regret bounds. We achieve lower regret with lower reward variances and more informative priors on them, which is precisely why we pay only for what is uncertain. This is the first result of its kind. Finally, we corroborate our theory with extensive experiments, which show the superiority of our variance-adaptive Bayesian algorithm over prior frequentist approaches. We also show that our approach is robust to model misspecification and can be applied with estimated priors.

We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or involve computationally expensive nested Markov chain Monte Carlo (MCMC) loops. In contrast, the proposed approach leverages stochastic averaging within a slow-fast system of stochastic differential equations (SDEs) to estimate intermediate scores along a diffusion path without training or inner-loop MCMC. Two algorithms are developed under this framework: MultALMC, which uses multiscale annealed Langevin dynamics, and MultCDiff, based on multiscale controlled diffusions for the reverse-time Ornstein-Uhlenbeck process. Both overdamped and underdamped variants are considered, with theoretical guarantees of convergence to the desired diffusion path. The framework is extended to handle heavy-tailed target distributions using Student's t-based noise models and tailored fast-process dynamics. Empirical results across synthetic and real-world benchmarks, including multimodal and high-dimensional distributions, demonstrate that the proposed methods are competitive with existing samplers in terms of accuracy and efficiency, without the need for learned models.

Generative modeling of time series is a central challenge in time series analysis, particularly under data-scarce conditions. Despite recent advances in generative modeling, a comprehensive understanding of how state-of-the-art generative models perform under limited supervision remains lacking. In this work, we conduct the first large-scale study evaluating leading generative models in data-scarce settings, revealing a substantial performance gap between full-data and data-scarce regimes. To close this gap, we propose a unified diffusion-based generative framework that can synthesize high-fidelity time series across diverse domains using just a few examples. Our model is pre-trained on a large, heterogeneous collection of time series datasets, enabling it to learn generalizable temporal representations. It further incorporates architectural innovations such as dynamic convolutional layers for flexible channel adaptation and dataset token conditioning for domain-aware generation. Without requiring abundant supervision, our unified model achieves state-of-the-art performance in few-shot settings-outperforming domain-specific baselines across a wide range of subset sizes. Remarkably, it also surpasses all baselines even when tested on full datasets benchmarks, highlighting the strength of pre-training and cross-domain generalization. We hope this work encourages the community to revisit few-shot generative modeling as a key problem in time series research and pursue unified solutions that scale efficiently across domains. Code is available at https://github.com/azencot-group/ImagenFew.

Despite substantial advances in scaling test-time compute, an ongoing debate in the community is how it should be scaled up to enable continued and efficient improvements with scaling. There are largely two approaches: first, distilling successful search or thinking traces; and second, using verification (e.g., 0/1 outcome rewards, reward models, or verifiers) to guide reinforcement learning (RL) and search algorithms. In this paper, we prove that finetuning LLMs with verifier-based (VB) methods based on RL or search is far superior to verifier-free (VF) approaches based on distilling or cloning search traces, given a fixed amount of compute/data budget. Further, we show that as we scale test-time compute (measured as the output token length) and training data, suboptimality of VF methods scales poorly compared to VB when the base pre-trained LLM presents a heterogeneous distribution over correct solution traces (e.g., different lengths, styles, etc.) and admits a non-sharp distribution over rewards on traces sampled from it. We formalize this condition using anti-concentration [Erdos, 1945]. This implies a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF methods widening as test-time budget grows. We corroborate our theory empirically on both didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.

Diffusion models have demonstrated impressive generative capabilities, but their exposure bias problem, described as the input mismatch between training and sampling, lacks in-depth exploration. In this paper, we systematically investigate the exposure bias problem in diffusion models by first analytically modelling the sampling distribution, based on which we then attribute the prediction error at each sampling step as the root cause of the exposure bias issue. Furthermore, we discuss potential solutions to this issue and propose an intuitive metric for it. Along with the elucidation of exposure bias, we propose a simple, yet effective, training-free method called Epsilon Scaling to alleviate the exposure bias. We show that Epsilon Scaling explicitly moves the sampling trajectory closer to the vector field learned in the training phase by scaling down the network output (Epsilon), mitigating the input mismatch between training and sampling. Experiments on various diffusion frameworks (ADM, DDPM/DDIM, EDM, LDM), unconditional and conditional settings, and deterministic vs. stochastic sampling verify the effectiveness of our method. Remarkably, our ADM-ES, as a SOTA stochastic sampler, obtains 2.17 FID on CIFAR-10 under 100-step unconditional generation. The code is available at https://github.com/forever208/ADM-ES and https://github.com/forever208/EDM-ES.

Visual Autoregressive (VAR) models have recently garnered significant attention for their innovative next-scale prediction paradigm, offering notable advantages in both inference efficiency and image quality compared to traditional multi-step autoregressive (AR) and diffusion models. However, despite their efficiency, VAR models often suffer from the diversity collapse i.e., a reduction in output variability, analogous to that observed in few-step distilled diffusion models. In this paper, we introduce DiverseVAR, a simple yet effective approach that restores the generative diversity of VAR models without requiring any additional training. Our analysis reveals the pivotal component of the feature map as a key factor governing diversity formation at early scales. By suppressing the pivotal component in the model input and amplifying it in the model output, DiverseVAR effectively unlocks the inherent generative potential of VAR models while preserving high-fidelity synthesis. Empirical results demonstrate that our approach substantially enhances generative diversity with only neglectable performance influences. Our code will be publicly released at https://github.com/wangtong627/DiverseVAR.

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

As hyperparameter tuning becomes increasingly costly at scale, efficient tuning methods are essential. Yet principles for guiding hyperparameter tuning remain limited. In this work, we seek to establish such principles by considering a broad range of hyperparameters, including batch size, learning rate, and weight decay. We identify a phenomenon we call trajectory invariance, where pre-training loss curves, gradient noise, and gradient norm exhibit invariance--closely overlapping--with respect to a quantity that combines learning rate and weight decay. This phenomenon effectively reduces the original two-dimensional hyperparameter space to one dimension, yielding an efficient tuning rule: follow the salient direction revealed by trajectory invariance. Furthermore, we refine previous scaling laws and challenge several existing viewpoints. Overall, our work proposes new principles for efficient tuning and inspires future research on scaling laws.

A range of recent optimizers have emerged that approximate the same "matrix-whitening" transformation in various ways. In this work, we systematically deconstruct such optimizers, aiming to disentangle the key components that explain performance. Across tuned hyperparameters across the board, all flavors of matrix-whitening methods reliably outperform elementwise counterparts, such as Adam. Matrix-whitening is often related to spectral descent -- however, experiments reveal that performance gains are *not explained solely by accurate spectral normalization* -- particularly, SOAP displays the largest per-step gain, even though Muon more accurately descends along the steepest spectral descent direction. Instead, we argue that matrix-whitening serves two purposes, and the variance adaptation component of matrix-whitening is the overlooked ingredient explaining this performance gap. Experiments show that variance-adapted versions of optimizers consistently outperform their sign-descent counterparts, including an adaptive version of Muon. We further ablate variance adaptation strategies, finding that while lookahead style approximations are not as effective, low-rank variance estimators can effectively reduce memory costs without a performance loss.

Evaluation benchmarks are the cornerstone of measuring capabilities of large language models (LLMs), as well as driving progress in said capabilities. Originally designed to make claims about capabilities (or lack thereof) in fully pretrained models, evaluation benchmarks are now also extensively used to decide between various training choices. Despite this widespread usage, we rarely quantify the variance in our evaluation benchmarks, which dictates whether differences in performance are meaningful. Here, we define and measure a range of metrics geared towards measuring variance in evaluation benchmarks, including seed variance across initialisations, and monotonicity during training. By studying a large number of models -- both openly available and pretrained from scratch -- we provide empirical estimates for a variety of variance metrics, with considerations and recommendations for practitioners. We also evaluate the utility and tradeoffs of continuous versus discrete performance measures and explore options for better understanding and reducing this variance. We find that simple changes, such as framing choice tasks (like MMLU) as completion tasks, can often reduce variance for smaller scale (sim7B) models, while more involved methods inspired from human testing literature (such as item analysis and item response theory) struggle to meaningfully reduce variance. Overall, our work provides insights into variance in evaluation benchmarks, suggests LM-specific techniques to reduce variance, and more generally encourages practitioners to carefully factor in variance when comparing models.

Large language models (LLMs) have achieved significant performance gains via scaling up model sizes and/or data. However, recent evidence suggests diminishing returns from such approaches, motivating scaling the computation spent at inference time. Existing inference-time scaling methods, usually with reward models, cast the task as a search problem, which tends to be vulnerable to reward hacking as a consequence of approximation errors in reward models. In this paper, we instead cast inference-time scaling as a probabilistic inference task and leverage sampling-based techniques to explore the typical set of the state distribution of a state-space model with an approximate likelihood, rather than optimize for its mode directly. We propose a novel inference-time scaling approach by adapting particle-based Monte Carlo methods to this task. Our empirical evaluation demonstrates that our methods have a 4-16x better scaling rate over our deterministic search counterparts on various challenging mathematical reasoning tasks. Using our approach, we show that Qwen2.5-Math-1.5B-Instruct can surpass GPT-4o accuracy in only 4 rollouts, while Qwen2.5-Math-7B-Instruct scales to o1 level accuracy in only 32 rollouts. Our work not only presents an effective method to inference-time scaling, but also connects the rich literature in probabilistic inference with inference-time scaling of LLMs to develop more robust algorithms in future work. Code and further information is available at https://probabilistic-inference-scaling.github.io.

This paper presents innovative enhancements to diffusion models by integrating a novel multi-resolution network and time-dependent layer normalization. Diffusion models have gained prominence for their effectiveness in high-fidelity image generation. While conventional approaches rely on convolutional U-Net architectures, recent Transformer-based designs have demonstrated superior performance and scalability. However, Transformer architectures, which tokenize input data (via "patchification"), face a trade-off between visual fidelity and computational complexity due to the quadratic nature of self-attention operations concerning token length. While larger patch sizes enable attention computation efficiency, they struggle to capture fine-grained visual details, leading to image distortions. To address this challenge, we propose augmenting the Diffusion model with the Multi-Resolution network (DiMR), a framework that refines features across multiple resolutions, progressively enhancing detail from low to high resolution. Additionally, we introduce Time-Dependent Layer Normalization (TD-LN), a parameter-efficient approach that incorporates time-dependent parameters into layer normalization to inject time information and achieve superior performance. Our method's efficacy is demonstrated on the class-conditional ImageNet generation benchmark, where DiMR-XL variants outperform prior diffusion models, setting new state-of-the-art FID scores of 1.70 on ImageNet 256 x 256 and 2.89 on ImageNet 512 x 512. Project page: https://qihao067.github.io/projects/DiMR

Recent innovations on hardware (e.g. Nvidia A100) have motivated learning N:M structured sparsity masks from scratch for fast model inference. However, state-of-the-art learning recipes in this regime (e.g. SR-STE) are proposed for non-adaptive optimizers like momentum SGD, while incurring non-trivial accuracy drop for Adam-trained models like attention-based LLMs. In this paper, we first demonstrate such gap origins from poorly estimated second moment (i.e. variance) in Adam states given by the masked weights. We conjecture that learning N:M masks with Adam should take the critical regime of variance estimation into account. In light of this, we propose STEP, an Adam-aware recipe that learns N:M masks with two phases: first, STEP calculates a reliable variance estimate (precondition phase) and subsequently, the variance remains fixed and is used as a precondition to learn N:M masks (mask-learning phase). STEP automatically identifies the switching point of two phases by dynamically sampling variance changes over the training trajectory and testing the sample concentration. Empirically, we evaluate STEP and other baselines such as ASP and SR-STE on multiple tasks including CIFAR classification, machine translation and LLM fine-tuning (BERT-Base, GPT-2). We show STEP mitigates the accuracy drop of baseline recipes and is robust to aggressive structured sparsity ratios.

Sampling-based algorithms, which eliminate ''unimportant'' computations during forward and/or back propagation (BP), offer potential solutions to accelerate neural network training. However, since sampling introduces approximations to training, such algorithms may not consistently maintain accuracy across various tasks. In this work, we introduce a variance-controlled adaptive sampling (VCAS) method designed to accelerate BP. VCAS computes an unbiased stochastic gradient with fine-grained layerwise importance sampling in data dimension for activation gradient calculation and leverage score sampling in token dimension for weight gradient calculation. To preserve accuracy, we control the additional variance by learning the sample ratio jointly with model parameters during training. We assessed VCAS on multiple fine-tuning and pre-training tasks in both vision and natural language domains. On all the tasks, VCAS can preserve the original training loss trajectory and validation accuracy with an up to 73.87% FLOPs reduction of BP and 49.58% FLOPs reduction of the whole training process. The implementation is available at https://github.com/thu-ml/VCAS .

The rapid advancement of video diffusion models has been hindered by fundamental limitations in temporal modeling, particularly the rigid synchronization of frame evolution imposed by conventional scalar timestep variables. While task-specific adaptations and autoregressive models have sought to address these challenges, they remain constrained by computational inefficiency, catastrophic forgetting, or narrow applicability. In this work, we present Pusa, a groundbreaking paradigm that leverages vectorized timestep adaptation (VTA) to enable fine-grained temporal control within a unified video diffusion framework. Besides, VTA is a non-destructive adaptation, which means it fully preserves the capabilities of the base model. By finetuning the SOTA Wan2.1-T2V-14B model with VTA, we achieve unprecedented efficiency -- surpassing the performance of Wan-I2V-14B with leq 1/200 of the training cost (\500 vs. \geq 100,000) and leq 1/2500 of the dataset size (4K vs. geq 10M samples). Pusa not only sets a new standard for image-to-video (I2V) generation, achieving a VBench-I2V total score of 87.32\% (vs. 86.86\% of Wan-I2V-14B), but also unlocks many zero-shot multi-task capabilities such as start-end frames and video extension -- all without task-specific training. Meanwhile, Pusa can still perform text-to-video generation. Mechanistic analyses reveal that our approach preserves the foundation model's generative priors while surgically injecting temporal dynamics, avoiding the combinatorial explosion inherent to vectorized timesteps. This work establishes a scalable, efficient, and versatile paradigm for next-generation video synthesis, democratizing high-fidelity video generation for research and industry alike. Code is open-sourced at https://github.com/Yaofang-Liu/Pusa-VidGen

We introduce TimeSeriesGym, a scalable benchmarking framework for evaluating Artificial Intelligence (AI) agents on time series machine learning engineering challenges. Existing benchmarks lack scalability, focus narrowly on model building in well-defined settings, and evaluate only a limited set of research artifacts (e.g., CSV submission files). To make AI agent benchmarking more relevant to the practice of machine learning engineering, our framework scales along two critical dimensions. First, recognizing that effective ML engineering requires a range of diverse skills, TimeSeriesGym incorporates challenges from diverse sources spanning multiple domains and tasks. We design challenges to evaluate both isolated capabilities (including data handling, understanding research repositories, and code translation) and their combinations, and rather than addressing each challenge independently, we develop tools that support designing multiple challenges at scale. Second, we implement evaluation mechanisms for multiple research artifacts, including submission files, code, and models, using both precise numeric measures and more flexible LLM-based evaluation approaches. This dual strategy balances objective assessment with contextual judgment. Although our initial focus is on time series applications, our framework can be readily extended to other data modalities, broadly enhancing the comprehensiveness and practical utility of agentic AI evaluation. We open-source our benchmarking framework to facilitate future research on the ML engineering capabilities of AI agents.

Test-time scaling (TTS) -- the dynamic allocation of compute during inference -- is a promising direction for improving reasoning in large language models (LLMs). However, a systematic comparison of well-known TTS strategies under identical conditions is missing, and the influence of model type and problem difficulty on performance remains unclear. To address these gaps, we conduct the first large-scale study of TTS, spanning over thirty billion tokens generated using eight open-source LLMs (7B to 235B parameters), across four reasoning datasets. We observe three consistent trends: (1) no single TTS strategy universally dominates; (2) reasoning models exhibit distinct trace-quality patterns across problem difficulty and trace length, forming short-horizon and long-horizon categories; and (3) for a given model type, the optimal TTS performance scales monotonically with compute budget. Based on these insights, we provide a practical recipe for selecting the best TTS strategy, considering problem difficulty, model type, and compute budget, providing a practical guide to effective inference-time scaling.

Test-Time Scaling (TTS) is a promising approach to progressively elicit the model's intelligence during inference. Recently, training-based TTS methods, such as continued reinforcement learning (RL), have further surged in popularity, while training-free TTS methods are gradually fading from prominence. However, the additional computation overhead of training amplifies the burden on test-time scaling. In this paper, we focus on training-free TTS methods for reasoning. We first design Conditional Step-level Self-refinement, a fine-grained sequential scaling method guided by process verification. On top of its effectiveness, we further combine it with other classical parallel scaling methods at the step level, to introduce a novel inference paradigm called Hybrid Test-Time Scaling. Extensive experiments on five instruction-tuned LLMs across different scales (3B-14B) and families demonstrate that hybrid strategy incorporating various training-free TTS methods at a fine granularity has considerable potential for expanding the reasoning performance boundaries of LLMs.

Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance tradeoffs. We theoretically show that, under some conditions, estimators such as MINE exhibit variance that could grow exponentially with the true amount of underlying MI. We also empirically demonstrate that existing estimators fail to satisfy basic self-consistency properties of MI, such as data processing and additivity under independence. Based on a unified perspective of variational approaches, we develop a new estimator that focuses on variance reduction. Empirical results on standard benchmark tasks demonstrate that our proposed estimator exhibits improved bias-variance trade-offs on standard benchmark tasks.

Recent advances in text-to-image generative models have enabled numerous practical applications, including subject-driven generation, which fine-tunes pretrained models to capture subject semantics from only a few examples. While diffusion-based models produce high-quality images, their extensive denoising steps result in significant computational overhead, limiting real-world applicability. Visual autoregressive~(VAR) models, which predict next-scale tokens rather than spatially adjacent ones, offer significantly faster inference suitable for practical deployment. In this paper, we propose the first VAR-based approach for subject-driven generation. However, na\"{\i}ve fine-tuning VAR leads to computational overhead, language drift, and reduced diversity. To address these challenges, we introduce selective layer tuning to reduce complexity and prior distillation to mitigate language drift. Additionally, we found that the early stages have a greater influence on the generation of subject than the latter stages, which merely synthesize local details. Based on this finding, we propose scale-wise weighted tuning, which prioritizes coarser resolutions for promoting the model to focus on the subject-relevant information instead of local details. Extensive experiments validate that our method significantly outperforms diffusion-based baselines across various metrics and demonstrates its practical usage.

Time series foundation models have demonstrated impressive performance as zero-shot forecasters. However, achieving effectively unified training on time series remains an open challenge. Existing approaches introduce some level of model specialization to account for the highly heterogeneous nature of time series data. For instance, Moirai pursues unified training by employing multiple input/output projection layers, each tailored to handle time series at a specific frequency. Similarly, TimesFM maintains a frequency embedding dictionary for this purpose. We identify two major drawbacks to this human-imposed frequency-level model specialization: (1) Frequency is not a reliable indicator of the underlying patterns in time series. For example, time series with different frequencies can display similar patterns, while those with the same frequency may exhibit varied patterns. (2) Non-stationarity is an inherent property of real-world time series, leading to varied distributions even within a short context window of a single time series. Frequency-level specialization is too coarse-grained to capture this level of diversity. To address these limitations, this paper introduces Moirai-MoE, using a single input/output projection layer while delegating the modeling of diverse time series patterns to the sparse mixture of experts (MoE) within Transformers. With these designs, Moirai-MoE reduces reliance on human-defined heuristics and enables automatic token-level specialization. Extensive experiments on 39 datasets demonstrate the superiority of Moirai-MoE over existing foundation models in both in-distribution and zero-shot scenarios. Furthermore, this study conducts comprehensive model analyses to explore the inner workings of time series MoE foundation models and provides valuable insights for future research.

Recent developments in large language models have shown advantages in reallocating a notable share of computational resource from training time to inference time. However, the principles behind inference time scaling are not well understood. In this paper, we introduce an analytically tractable model of inference-time scaling: Bayesian linear regression with a reward-weighted sampler, where the reward is determined from a linear model, modeling LLM-as-a-judge scenario. We study this problem in the high-dimensional regime, where the deterministic equivalents dictate a closed-form expression for the posterior predictive mean and variance. We analyze the generalization error when training data are sampled from a teacher model. We draw k inference-time samples and select via softmax at a temperature applied to a quadratic reward. When the reward is not too different from the teacher, the generalization error decreases monotonically with increasing inference time samples k. However, the specific reward that optimizes inference-time selection generally differs from the teacher. In contrast, substantial reward misspecification induces a finite optimal k beyond which more sampling can increase the generalization error. For fixed k, there exists an optimal sampling temperature. We experimentally verify these facts in large language model inference with an additional large language model as a judge. In the "best-of-k" limit with the teacher as reward, we theoretically show that the generalization error decays as Θ(1/k^2) and determine the leading coefficient via extreme value theory. These formulas delineate domains where scaling inference-time computation is provably preferable to collecting more data. Finally, we demonstrate that when task difficulty increases, the previously mentioned advantage of inference-time compute degrades.

The Diffusion models, widely used for image generation, face significant challenges related to their broad applicability due to prolonged inference times and high memory demands. Efficient Post-Training Quantization (PTQ) is crucial to address these issues. However, unlike traditional models, diffusion models critically rely on the time-step for the multi-round denoising. Typically, each time-step is encoded into a hypersensitive temporal feature by several modules. Despite this, existing PTQ methods do not optimize these modules individually. Instead, they employ unsuitable reconstruction objectives and complex calibration methods, leading to significant disturbances in the temporal feature and denoising trajectory, as well as reduced compression efficiency. To address these challenges, we introduce a novel quantization framework that includes three strategies: 1) TIB-based Maintenance: Based on our innovative Temporal Information Block (TIB) definition, Temporal Information-aware Reconstruction (TIAR) and Finite Set Calibration (FSC) are developed to efficiently align original temporal features. 2) Cache-based Maintenance: Instead of indirect and complex optimization for the related modules, pre-computing and caching quantized counterparts of temporal features are developed to minimize errors. 3) Disturbance-aware Selection: Employ temporal feature errors to guide a fine-grained selection between the two maintenance strategies for further disturbance reduction. This framework preserves most of the temporal information and ensures high-quality end-to-end generation. Extensive testing on various datasets, diffusion models and hardware confirms our superior performance and acceleration..

Stochastic latent variable models (LVMs) achieve state-of-the-art performance on natural image generation but are still inferior to deterministic models on speech. In this paper, we develop a speech benchmark of popular temporal LVMs and compare them against state-of-the-art deterministic models. We report the likelihood, which is a much used metric in the image domain, but rarely, or incomparably, reported for speech models. To assess the quality of the learned representations, we also compare their usefulness for phoneme recognition. Finally, we adapt the Clockwork VAE, a state-of-the-art temporal LVM for video generation, to the speech domain. Despite being autoregressive only in latent space, we find that the Clockwork VAE can outperform previous LVMs and reduce the gap to deterministic models by using a hierarchy of latent variables.

Time series foundation models (TSFMs) have recently gained significant attention due to their strong zero-shot capabilities and widespread real-world applications. Such models typically require a computationally costly pretraining on large-scale, carefully curated collections of real-world sequences. To allow for a sample-efficient pretraining of TSFMs, we propose CauKer, a novel algorithm designed to generate diverse, causally coherent synthetic time series with realistic trends, seasonality, and nonlinear interactions. CauKer combines Gaussian Process (GP) kernel composition with Structural Causal Models (SCM) to produce data for sample-efficient pretraining of state-of-the-art classification TSFMs having different architectures and following different pretraining approaches. Additionally, our experiments reveal that CauKer-generated datasets exhibit clear scaling laws for both dataset size (10K to 10M samples) and model capacity (1M to 783M parameters), unlike real-world datasets, which display irregular scaling behavior.

Recently, channel-independent methods have achieved state-of-the-art performance in multivariate time series (MTS) forecasting. Despite reducing overfitting risks, these methods miss potential opportunities in utilizing channel dependence for accurate predictions. We argue that there exist locally stationary lead-lag relationships between variates, i.e., some lagged variates may follow the leading indicators within a short time period. Exploiting such channel dependence is beneficial since leading indicators offer advance information that can be used to reduce the forecasting difficulty of the lagged variates. In this paper, we propose a new method named LIFT that first efficiently estimates leading indicators and their leading steps at each time step and then judiciously allows the lagged variates to utilize the advance information from leading indicators. LIFT plays as a plugin that can be seamlessly collaborated with arbitrary time series forecasting methods. Extensive experiments on six real-world datasets demonstrate that LIFT improves the state-of-the-art methods by 5.5% in average forecasting performance. Our code is available at https://github.com/SJTU-Quant/LIFT.

Time series foundation models (TSFMs) offer strong zero-shot forecasting via large-scale pre-training, yet fine-tuning remains critical for boosting performance in domains with limited public data. With the growing number of TSFMs, efficiently identifying the best model for downstream fine-tuning becomes increasingly challenging. In this work, we introduce TimeTic, a transferability estimation framework that recasts model selection as an in-context-learning problem: given observations on known (source) datasets, it predicts how a TSFM will perform after fine-tuning on a downstream (target) dataset. TimeTic flexibly organizes the observed model-data relationships as contextual information, allowing it to adapt seamlessly to various test-time scenarios. Leveraging the natural tabular structure formed by dataset meta-features, model characteristics, and fine-tuned performance, we employ tabular foundation models to serve as in-context learners. We further introduce a novel model characterization based on entropy evolution across model layers, capturing embedding-space distinctions and enabling TimeTic to generalize across arbitrary model sets. We establish a comprehensive benchmark for transferability estimation including 10 datasets, 10 foundation models, and 3 forecasting tasks. On this benchmark, TimeTic's estimation demonstrates strong alignment with actual fine-tuned performance for previously unseen datasets, achieving a mean rank correlation of approximately 0.6 and a 30% improvement compared to using zero-shot performance as the transferability score.

The outcome of Large Language Model (LLM) pre-training strongly depends on weight initialization and variance control strategies. Although the importance of initial variance control has been well documented in neural networks in general, the literature on initialization and management of its growth during LLM pre-training, specifically, is somewhat sparse. In this paper, we introduce the Layer Index Rescaling (LIR) weight initialization scheme, and the Target Variance Rescaling (TVR) variance control strategy. Experiments on a 1B parameter LLaMA model demonstrate that better variance management using these techniques yields substantial improvements in downstream task performance (up to 4.6% on common pre-training benchmarks) and reduces extreme activation values, thus mitigating challenges associated with quantization and low-precision training. Our code is available at: https://github.com/bluorion-com/weight_rescaling.

Control variates are variance reduction tools for Monte Carlo estimators. They can provide significant variance reduction, but usually require a large number of samples, which can be prohibitive when sampling or evaluating the integrand is computationally expensive. Furthermore, there are many scenarios where we need to compute multiple related integrals simultaneously or sequentially, which can further exacerbate computational costs. In this paper, we propose vector-valued control variates, an extension of control variates which can be used to reduce the variance of multiple Monte Carlo estimators jointly. This allows for the transfer of information across integration tasks, and hence reduces the need for a large number of samples. We focus on control variates based on kernel interpolants and our novel construction is obtained through a generalised Stein identity and the development of novel matrix-valued Stein reproducing kernels. We demonstrate our methodology on a range of problems including multifidelity modelling, Bayesian inference for dynamical systems, and model evidence computation through thermodynamic integration.

Empirical scaling laws prescribe how to allocate parameters, data, and compute, while maximal-update parameterization (muP) enables learning-rate transfer across widths by equalizing early-time update magnitudes. However, in modern scale-invariant architectures, training quickly enters an optimizer-governed steady state where normalization layers create backward scale sensitivity and the effective learning rate becomes width dependent, degrading muP transfer. We address this by introducing a weight-decay scaling rule for AdamW that preserves sublayer gain across widths. Empirically, the singular-value spectrum of each matrix parameter scales in norm as eta/lambda with an approximately invariant shape; under width scaling d, we observe that the top singular value scales approximately as eta/lambdacdot d^{0.75}. Combining this observation with the muP learning-rate rule eta_2propto d^{-1} for matrix-like parameters implies an empirical weight-decay scaling rule lambda_2propto d that approximately keeps sublayer gains width invariant. Together with vector-like parameters trained at eta_1=Theta_d(1) and lambda_1=0, this yields zero-shot transfer of both learning rate and weight decay from proxy to target widths, removing per-width sweeps. We validate the rule on LLaMA-style Transformers and in a minimal synthetic setting, and we provide a simple diagnostic, matching top singular values, to check sublayer-gain invariance. Our results extend muP beyond the near-init regime by explicitly controlling steady-state scales set by the optimizer, offering a practical recipe for width-robust hyperparameter transfer under AdamW.

Generative models have made significant impacts across various domains, largely due to their ability to scale during training by increasing data, computational resources, and model size, a phenomenon characterized by the scaling laws. Recent research has begun to explore inference-time scaling behavior in Large Language Models (LLMs), revealing how performance can further improve with additional computation during inference. Unlike LLMs, diffusion models inherently possess the flexibility to adjust inference-time computation via the number of denoising steps, although the performance gains typically flatten after a few dozen. In this work, we explore the inference-time scaling behavior of diffusion models beyond increasing denoising steps and investigate how the generation performance can further improve with increased computation. Specifically, we consider a search problem aimed at identifying better noises for the diffusion sampling process. We structure the design space along two axes: the verifiers used to provide feedback, and the algorithms used to find better noise candidates. Through extensive experiments on class-conditioned and text-conditioned image generation benchmarks, our findings reveal that increasing inference-time compute leads to substantial improvements in the quality of samples generated by diffusion models, and with the complicated nature of images, combinations of the components in the framework can be specifically chosen to conform with different application scenario.

Modeling latent variables with priors and hyperpriors is an essential problem in variational image compression. Formally, trade-off between rate and distortion is handled well if priors and hyperpriors precisely describe latent variables. Current practices only adopt univariate priors and process each variable individually. However, we find inter-correlations and intra-correlations exist when observing latent variables in a vectorized perspective. These findings reveal visual redundancies to improve rate-distortion performance and parallel processing ability to speed up compression. This encourages us to propose a novel vectorized prior. Specifically, a multivariate Gaussian mixture is proposed with means and covariances to be estimated. Then, a novel probabilistic vector quantization is utilized to effectively approximate means, and remaining covariances are further induced to a unified mixture and solved by cascaded estimation without context models involved. Furthermore, codebooks involved in quantization are extended to multi-codebooks for complexity reduction, which formulates an efficient compression procedure. Extensive experiments on benchmark datasets against state-of-the-art indicate our model has better rate-distortion performance and an impressive 3.18times compression speed up, giving us the ability to perform real-time, high-quality variational image compression in practice. Our source code is publicly available at https://github.com/xiaosu-zhu/McQuic.

Deep neural networks, including transformers and convolutional neural networks, have significantly improved multivariate time series classification (MTSC). However, these methods often rely on supervised learning, which does not fully account for the sparsity and locality of patterns in time series data (e.g., diseases-related anomalous points in ECG). To address this challenge, we formally reformulate MTSC as a weakly supervised problem, introducing a novel multiple-instance learning (MIL) framework for better localization of patterns of interest and modeling time dependencies within time series. Our novel approach, TimeMIL, formulates the temporal correlation and ordering within a time-aware MIL pooling, leveraging a tokenized transformer with a specialized learnable wavelet positional token. The proposed method surpassed 26 recent state-of-the-art methods, underscoring the effectiveness of the weakly supervised TimeMIL in MTSC. The code will be available at https://github.com/xiwenc1/TimeMIL.

Masked autoencoders (MAEs) are increasingly applied to electronic health records (EHR) for learning general-purpose representations that support diverse clinical tasks. However, existing approaches typically rely on uniform random masking, implicitly assuming all features are equally predictable. In reality, laboratory tests exhibit substantial heterogeneity in volatility: some biomarkers (e.g., sodium) remain stable, while others (e.g., lactate) fluctuate considerably and are more difficult to model. Clinically, volatile biomarkers often signal acute pathophysiology and require more sophisticated modeling to capture their complex temporal patterns. We propose a volatility-aware pretraining strategy, Coefficient of Variation Masking (CV-Masking), that adaptively adjusts masking probabilities according to the intrinsic variability of each feature. Combined with a value-only masking objective aligned with clinical workflows, CV-Masking yields systematic improvements over random and variance-based strategies. Experiments on a large panel of laboratory tests show that CV-Masking enhances reconstruction, improves downstream predictive performance, and accelerates convergence, producing more robust and clinically meaningful EHR representations.

Current architectures for video understanding mainly build upon 3D convolutional blocks or 2D convolutions with additional operations for temporal modeling. However, these methods all regard the temporal axis as a separate dimension of the video sequence, which requires large computation and memory budgets and thus limits their usage on mobile devices. In this paper, we propose to squeeze the time axis of a video sequence into the channel dimension and present a lightweight video recognition network, term as SqueezeTime, for mobile video understanding. To enhance the temporal modeling capability of the proposed network, we design a Channel-Time Learning (CTL) Block to capture temporal dynamics of the sequence. This module has two complementary branches, in which one branch is for temporal importance learning and another branch with temporal position restoring capability is to enhance inter-temporal object modeling ability. The proposed SqueezeTime is much lightweight and fast with high accuracies for mobile video understanding. Extensive experiments on various video recognition and action detection benchmarks, i.e., Kinetics400, Kinetics600, HMDB51, AVA2.1 and THUMOS14, demonstrate the superiority of our model. For example, our SqueezeTime achieves +1.2% accuracy and +80% GPU throughput gain on Kinetics400 than prior methods. Codes are publicly available at https://github.com/xinghaochen/SqueezeTime and https://github.com/mindspore-lab/models/tree/master/research/huawei-noah/SqueezeTime.

Efficient LLM pre-training requires well-tuned hyperparameters (HPs), including learning rate {\eta} and weight decay {\lambda}. We study scaling laws for HPs: formulas for how to scale HPs as we scale model size N, dataset size D, and batch size B. Recent work suggests the AdamW timescale, B/({\eta}{\lambda}D), should remain constant across training settings, and we verify the implication that optimal {\lambda} scales linearly with B, for a fixed N,D. However, as N,D scale, we show the optimal timescale obeys a precise power law in the tokens-per-parameter ratio, D/N. This law thus provides a method to accurately predict {\lambda}opt in advance of large-scale training. We also study scaling laws for optimal batch size Bopt (the B enabling lowest loss at a given N,D) and critical batch size Bcrit (the B beyond which further data parallelism becomes ineffective). In contrast with prior work, we find both Bopt and Bcrit scale as power laws in D, independent of model size, N. Finally, we analyze how these findings inform the real-world selection of Pareto-optimal N and D under dual training time and compute objectives.

Cloud platforms are increasingly relied upon to host diverse, resource-intensive workloads due to their scalability, flexibility, and cost-efficiency. In multi-tenant cloud environments, virtual machines are consolidated on shared physical servers to improve resource utilization. While virtualization guarantees resource partitioning for CPU, memory, and storage, it cannot ensure performance isolation. Competition for shared resources such as last-level cache, memory bandwidth, and network interfaces often leads to severe performance degradation. Existing management techniques, including VM scheduling and resource provisioning, require accurate performance prediction to mitigate interference. However, this remains challenging in public clouds due to the black-box nature of VMs and the highly dynamic nature of workloads. To address these limitations, we propose CloudFormer, a dual-branch Transformer-based model designed to predict VM performance degradation in black-box environments. CloudFormer jointly models temporal dynamics and system-level interactions, leveraging 206 system metrics at one-second resolution across both static and dynamic scenarios. This design enables the model to capture transient interference effects and adapt to varying workload conditions without scenario-specific tuning. Complementing the methodology, we provide a fine-grained dataset that significantly expands the temporal resolution and metric diversity compared to existing benchmarks. Experimental results demonstrate that CloudFormer consistently outperforms state-of-the-art baselines across multiple evaluation metrics, achieving robust generalization across diverse and previously unseen workloads. Notably, CloudFormer attains a mean absolute error (MAE) of just 7.8%, representing a substantial improvement in predictive accuracy and outperforming existing methods at least by 28%.

Denoising diffusion models have recently shown impressive results in generative tasks. By learning powerful priors from huge collections of training images, such models are able to gradually modify complete noise to a clean natural image via a sequence of small denoising steps, seemingly making them well-suited for single image denoising. However, effectively applying denoising diffusion models to removal of realistic noise is more challenging than it may seem, since their formulation is based on additive white Gaussian noise, unlike noise in real-world images. In this work, we present SVNR, a novel formulation of denoising diffusion that assumes a more realistic, spatially-variant noise model. SVNR enables using the noisy input image as the starting point for the denoising diffusion process, in addition to conditioning the process on it. To this end, we adapt the diffusion process to allow each pixel to have its own time embedding, and propose training and inference schemes that support spatially-varying time maps. Our formulation also accounts for the correlation that exists between the condition image and the samples along the modified diffusion process. In our experiments we demonstrate the advantages of our approach over a strong diffusion model baseline, as well as over a state-of-the-art single image denoising method.

There has been a recent surge of interest in time series modeling using the Transformer architecture. However, forecasting multivariate time series with Transformer presents a unique challenge as it requires modeling both temporal (cross-time) and variate (cross-variate) dependencies. While Transformer-based models have gained popularity for their flexibility in capturing both sequential and cross-variate relationships, it is unclear how to best integrate these two sources of information in the context of the Transformer architecture while optimizing for both performance and efficiency. We re-purpose the Transformer architecture to effectively model both cross-time and cross-variate dependencies. Our approach begins by embedding each variate independently into a variate-wise representation that captures its cross-time dynamics, and then models cross-variate dependencies through attention mechanisms on these learned embeddings. Gating operations in both cross-time and cross-variate modeling phases regulate information flow, allowing the model to focus on the most relevant features for accurate predictions. Our method achieves state-of-the-art performance across 13 real-world datasets and can be seamlessly integrated into other Transformer-based and LLM-based forecasters, delivering performance improvements up to 20.7\% over original models. Code is available at this repository: https://github.com/nyuolab/Gateformer.

Multivariate time series forecasting is essential in domains such as finance, transportation, climate, and energy. However, existing patch-based methods typically adopt fixed-length segmentation, overlooking the heterogeneity of local temporal dynamics and the decoding heterogeneity of forecasting. Such designs lose details in information-dense regions, introduce redundancy in stable segments, and fail to capture the distinct complexities of short-term and long-term horizons. We propose TimeMosaic, a forecasting framework that aims to address temporal heterogeneity. TimeMosaic employs adaptive patch embedding to dynamically adjust granularity according to local information density, balancing motif reuse with structural clarity while preserving temporal continuity. In addition, it introduces segment-wise decoding that treats each prediction horizon as a related subtask and adapts to horizon-specific difficulty and information requirements, rather than applying a single uniform decoder. Extensive evaluations on benchmark datasets demonstrate that TimeMosaic delivers consistent improvements over existing methods, and our model trained on the large-scale corpus with 321 billion observations achieves performance competitive with state-of-the-art TSFMs.

A central problem in learning from sequential data is representing cumulative history in an incremental fashion as more data is processed. We introduce a general framework (HiPPO) for the online compression of continuous signals and discrete time series by projection onto polynomial bases. Given a measure that specifies the importance of each time step in the past, HiPPO produces an optimal solution to a natural online function approximation problem. As special cases, our framework yields a short derivation of the recent Legendre Memory Unit (LMU) from first principles, and generalizes the ubiquitous gating mechanism of recurrent neural networks such as GRUs. This formal framework yields a new memory update mechanism (HiPPO-LegS) that scales through time to remember all history, avoiding priors on the timescale. HiPPO-LegS enjoys the theoretical benefits of timescale robustness, fast updates, and bounded gradients. By incorporating the memory dynamics into recurrent neural networks, HiPPO RNNs can empirically capture complex temporal dependencies. On the benchmark permuted MNIST dataset, HiPPO-LegS sets a new state-of-the-art accuracy of 98.3%. Finally, on a novel trajectory classification task testing robustness to out-of-distribution timescales and missing data, HiPPO-LegS outperforms RNN and neural ODE baselines by 25-40% accuracy.

Visual Autoregressive (VAR) has emerged as a promising approach in image generation, offering competitive potential and performance comparable to diffusion-based models. However, current AR-based visual generation models require substantial computational resources, limiting their applicability on resource-constrained devices. To address this issue, we conducted analysis and identified significant redundancy in three dimensions of the VAR model: (1) the attention map, (2) the attention outputs when using classifier free guidance, and (3) the data precision. Correspondingly, we proposed efficient attention mechanism and low-bit quantization method to enhance the efficiency of VAR models while maintaining performance. With negligible performance lost (less than 0.056 FID increase), we could achieve 85.2% reduction in attention computation, 50% reduction in overall memory and 1.5x latency reduction. To ensure deployment feasibility, we developed efficient training-free compression techniques and analyze the deployment feasibility and efficiency gain of each technique.

Scaling test-time compute is a promising axis for improving LLM capabilities. However, test-time compute can be scaled in a variety of ways, and effectively combining different approaches remains an active area of research. Here, we explore this problem in the context of solving real-world GitHub issues from the SWE-bench dataset. Our system, named CodeMonkeys, allows models to iteratively edit a codebase by jointly generating and running a testing script alongside their draft edit. We sample many of these multi-turn trajectories for every issue to generate a collection of candidate edits. This approach lets us scale "serial" test-time compute by increasing the number of iterations per trajectory and "parallel" test-time compute by increasing the number of trajectories per problem. With parallel scaling, we can amortize up-front costs across multiple downstream samples, allowing us to identify relevant codebase context using the simple method of letting an LLM read every file. In order to select between candidate edits, we combine voting using model-generated tests with a final multi-turn trajectory dedicated to selection. Overall, CodeMonkeys resolves 57.4% of issues from SWE-bench Verified using a budget of approximately 2300 USD. Our selection method can also be used to combine candidates from different sources. Selecting over an ensemble of edits from existing top SWE-bench Verified submissions obtains a score of 66.2% and outperforms the best member of the ensemble on its own. We fully release our code and data at https://scalingintelligence.stanford.edu/pubs/codemonkeys.

Nowadays, with the rising number of sensors in sectors such as healthcare and industry, the problem of multivariate time series classification (MTSC) is getting increasingly relevant and is a prime target for machine and deep learning approaches. Their expanding adoption in real-world environments is causing a shift in focus from the pursuit of ever-higher prediction accuracy with complex models towards practical, deployable solutions that balance accuracy and parameters such as prediction speed. An MTSC model that has attracted attention recently is ROCKET, based on random convolutional kernels, both because of its very fast training process and its state-of-the-art accuracy. However, the large number of features it utilizes may be detrimental to inference time. Examining its theoretical background and limitations enables us to address potential drawbacks and present LightWaveS: a framework for accurate MTSC, which is fast both during training and inference. Specifically, utilizing wavelet scattering transformation and distributed feature selection, we manage to create a solution that employs just 2.5% of the ROCKET features, while achieving accuracy comparable to recent MTSC models. LightWaveS also scales well across multiple compute nodes and with the number of input channels during training. In addition, it can significantly reduce the input size and provide insight to an MTSC problem by keeping only the most useful channels. We present three versions of our algorithm and their results on distributed training time and scalability, accuracy, and inference speedup. We show that we achieve speedup ranging from 9x to 53x compared to ROCKET during inference on an edge device, on datasets with comparable accuracy.

Diffusion models have achieved remarkable success across various domains. However, their slow generation speed remains a critical challenge. Existing acceleration methods, while aiming to reduce steps, often compromise sample quality, controllability, or introduce training complexities. Therefore, we propose RayFlow, a novel diffusion framework that addresses these limitations. Unlike previous methods, RayFlow guides each sample along a unique path towards an instance-specific target distribution. This method minimizes sampling steps while preserving generation diversity and stability. Furthermore, we introduce Time Sampler, an importance sampling technique to enhance training efficiency by focusing on crucial timesteps. Extensive experiments demonstrate RayFlow's superiority in generating high-quality images with improved speed, control, and training efficiency compared to existing acceleration techniques.

Test-time scaling (TTS), which involves dynamic allocation of compute during inference, offers a promising way to improve reasoning in large language models. While existing TTS methods work well, they often rely on long decoding paths or require a large number of samples to be generated, increasing the token usage and inference latency. We observe the surprising fact that for reasoning tasks, shorter traces are much more likely to be correct than longer ones. Motivated by this, we introduce First Finish Search (FFS), a training-free parallel decoding strategy that launches n independent samples and returns as soon as any one completes. We evaluate FFS alongside simple decoding, beam search, majority voting, and budget forcing on four reasoning models (DeepSeek-R1, R1-Distill-Qwen-32B, QwQ-32B and Phi-4-Reasoning-Plus) and across four datasets (AIME24, AIME25-I, AIME25-II and GPQA Diamond). With DeepSeek-R1, FFS achieves 82.23% accuracy on the AIME datasets, a 15% improvement over DeepSeek-R1's standalone accuracy, nearly matching OpenAI's o4-mini performance. Our theoretical analysis explains why stopping at the shortest trace is likely to yield a correct answer and identifies the conditions under which early stopping may be suboptimal. The elegance and simplicity of FFS demonstrate that straightforward TTS strategies can perform remarkably well, revealing the untapped potential of simple approaches at inference time.

Large reasoning models (LRMs) have exhibited the capacity of enhancing reasoning performance via internal test-time scaling. Building upon this, a promising direction is to further scale test-time compute to unlock even greater reasoning capabilities. However, as we push these scaling boundaries, systematically understanding the practical limits and achieving optimal resource allocation becomes a critical challenge. In this paper, we investigate the scaling Pareto of test-time scaling and introduce the Test-Time Scaling Performance Model (TTSPM). We theoretically analyze two fundamental paradigms for such extended scaling, parallel scaling and sequential scaling, from a probabilistic modeling perspective. Our primary contribution is the derivation of the saturation point on the scaling budget for both strategies, identifying thresholds beyond which additional computation yields diminishing returns. Remarkably, despite their distinct mechanisms, both paradigms converge to a unified mathematical structure in their upper bounds. We empirically validate our theoretical findings on challenging reasoning benchmarks, including AIME, MATH-500, and GPQA, demonstrating the practical utility of these bounds for test-time resource allocation. We hope that this work provides insights into the cost-benefit trade-offs of test-time scaling, guiding the development of more resource-efficient inference strategies for large reasoning models.

This paper does not introduce a novel method but instead establishes a straightforward, incremental, yet essential baseline for video temporal grounding (VTG), a core capability in video understanding. While multimodal large language models (MLLMs) excel at various video understanding tasks, the recipes for optimizing them for VTG remain under-explored. In this paper, we present TimeLens, a systematic investigation into building MLLMs with strong VTG ability, along two primary dimensions: data quality and algorithmic design. We first expose critical quality issues in existing VTG benchmarks and introduce TimeLens-Bench, comprising meticulously re-annotated versions of three popular benchmarks with strict quality criteria. Our analysis reveals dramatic model re-rankings compared to legacy benchmarks, confirming the unreliability of prior evaluation standards. We also address noisy training data through an automated re-annotation pipeline, yielding TimeLens-100K, a large-scale, high-quality training dataset. Building on our data foundation, we conduct in-depth explorations of algorithmic design principles, yielding a series of meaningful insights and effective yet efficient practices. These include interleaved textual encoding for time representation, a thinking-free reinforcement learning with verifiable rewards (RLVR) approach as the training paradigm, and carefully designed recipes for RLVR training. These efforts culminate in TimeLens models, a family of MLLMs with state-of-the-art VTG performance among open-source models and even surpass proprietary models such as GPT-5 and Gemini-2.5-Flash. All codes, data, and models will be released to facilitate future research.

Federated learning algorithms, such as FedAvg, are negatively affected by data heterogeneity and partial client participation. To mitigate the latter problem, global variance reduction methods, like FedVARP, leverage stale model updates for non-participating clients. These methods are effective under homogeneous client participation. Yet, this paper shows that, when some clients participate much less than others, aggregating updates with different levels of staleness can detrimentally affect the training process. Motivated by this observation, we introduce FedStale, a novel algorithm that updates the global model in each round through a convex combination of "fresh" updates from participating clients and "stale" updates from non-participating ones. By adjusting the weight in the convex combination, FedStale interpolates between FedAvg, which only uses fresh updates, and FedVARP, which treats fresh and stale updates equally. Our analysis of FedStale convergence yields the following novel findings: i) it integrates and extends previous FedAvg and FedVARP analyses to heterogeneous client participation; ii) it underscores how the least participating client influences convergence error; iii) it provides practical guidelines to best exploit stale updates, showing that their usefulness diminishes as data heterogeneity decreases and participation heterogeneity increases. Extensive experiments featuring diverse levels of client data and participation heterogeneity not only confirm these findings but also show that FedStale outperforms both FedAvg and FedVARP in many settings.

As a fundamental backbone for video generation, diffusion models are challenged by low inference speed due to the sequential nature of denoising. Previous methods speed up the models by caching and reusing model outputs at uniformly selected timesteps. However, such a strategy neglects the fact that differences among model outputs are not uniform across timesteps, which hinders selecting the appropriate model outputs to cache, leading to a poor balance between inference efficiency and visual quality. In this study, we introduce Timestep Embedding Aware Cache (TeaCache), a training-free caching approach that estimates and leverages the fluctuating differences among model outputs across timesteps. Rather than directly using the time-consuming model outputs, TeaCache focuses on model inputs, which have a strong correlation with the modeloutputs while incurring negligible computational cost. TeaCache first modulates the noisy inputs using the timestep embeddings to ensure their differences better approximating those of model outputs. TeaCache then introduces a rescaling strategy to refine the estimated differences and utilizes them to indicate output caching. Experiments show that TeaCache achieves up to 4.41x acceleration over Open-Sora-Plan with negligible (-0.07% Vbench score) degradation of visual quality.

Time series data are ubiquitous across a wide range of real-world domains. While real-world time series analysis (TSA) requires human experts to integrate numerical series data with multimodal domain-specific knowledge, most existing TSA models rely solely on numerical data, overlooking the significance of information beyond numerical series. This oversight is due to the untapped potential of textual series data and the absence of a comprehensive, high-quality multimodal dataset. To overcome this obstacle, we introduce Time-MMD, the first multi-domain, multimodal time series dataset covering 9 primary data domains. Time-MMD ensures fine-grained modality alignment, eliminates data contamination, and provides high usability. Additionally, we develop MM-TSFlib, the first multimodal time-series forecasting (TSF) library, seamlessly pipelining multimodal TSF evaluations based on Time-MMD for in-depth analyses. Extensive experiments conducted on Time-MMD through MM-TSFlib demonstrate significant performance enhancements by extending unimodal TSF to multimodality, evidenced by over 15% mean squared error reduction in general, and up to 40% in domains with rich textual data. More importantly, our datasets and library revolutionize broader applications, impacts, research topics to advance TSA. The dataset and library are available at https://github.com/AdityaLab/Time-MMD and https://github.com/AdityaLab/MM-TSFlib.

We present a novel variational framework for performing inference in (neural) stochastic differential equations (SDEs) driven by Markov-approximate fractional Brownian motion (fBM). SDEs offer a versatile tool for modeling real-world continuous-time dynamic systems with inherent noise and randomness. Combining SDEs with the powerful inference capabilities of variational methods, enables the learning of representative function distributions through stochastic gradient descent. However, conventional SDEs typically assume the underlying noise to follow a Brownian motion (BM), which hinders their ability to capture long-term dependencies. In contrast, fractional Brownian motion (fBM) extends BM to encompass non-Markovian dynamics, but existing methods for inferring fBM parameters are either computationally demanding or statistically inefficient. In this paper, building upon the Markov approximation of fBM, we derive the evidence lower bound essential for efficient variational inference of posterior path measures, drawing from the well-established field of stochastic analysis. Additionally, we provide a closed-form expression to determine optimal approximation coefficients. Furthermore, we propose the use of neural networks to learn the drift, diffusion and control terms within our variational posterior, leading to the variational training of neural-SDEs. In this framework, we also optimize the Hurst index, governing the nature of our fractional noise. Beyond validation on synthetic data, we contribute a novel architecture for variational latent video prediction,-an approach that, to the best of our knowledge, enables the first variational neural-SDE application to video perception.

The task of video generation requires synthesizing visually realistic and temporally coherent video frames. Existing methods primarily use asynchronous auto-regressive models or synchronous diffusion models to address this challenge. However, asynchronous auto-regressive models often suffer from inconsistencies between training and inference, leading to issues such as error accumulation, while synchronous diffusion models are limited by their reliance on rigid sequence length. To address these issues, we introduce Auto-Regressive Diffusion (AR-Diffusion), a novel model that combines the strengths of auto-regressive and diffusion models for flexible, asynchronous video generation. Specifically, our approach leverages diffusion to gradually corrupt video frames in both training and inference, reducing the discrepancy between these phases. Inspired by auto-regressive generation, we incorporate a non-decreasing constraint on the corruption timesteps of individual frames, ensuring that earlier frames remain clearer than subsequent ones. This setup, together with temporal causal attention, enables flexible generation of videos with varying lengths while preserving temporal coherence. In addition, we design two specialized timestep schedulers: the FoPP scheduler for balanced timestep sampling during training, and the AD scheduler for flexible timestep differences during inference, supporting both synchronous and asynchronous generation. Extensive experiments demonstrate the superiority of our proposed method, which achieves competitive and state-of-the-art results across four challenging benchmarks.